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**********  CLOtlRl 

Counterpoint 

STUDIES    IN    PART-WRITING 

BY 

WALTER  R.  SPALDING 

Assistant  Professor  of  Music 
in  Harvard  University 

00 

<4|£ 

PRICE,   TWO    DOLLARS 

Hrtbur  p.  Scbmibt 

BOSTON                LEIPZIG                NEWYORK 
120   Boylston  St.                                                                 136  Fifth  Avenue 

.  .    :  -     i    v 

Copyright,  1904,  by  ARTHUR  P.  SCHMIDT 


M  T  5  5 
S    7;- 


L  &  and  1.  C.  A. 


PREFACE 


On  the  subject  of  "  Counterpoint,"  as  that  term  is  generally 
understood,  this  book  does  not  profess  to  be  an  exhaustive  treatise. 
Rather  is  it  intended,  as  a  practical  textbook,  to  deal  with  the 
principles  of  free  part-writing  and  to  offer  suggestions  for  the  culti- 
vation of  such  a  musical  instinct  that  wherever  polyphony  *  is  desir- 
able in  composition  the  various  parts  shall  be  made  interesting  and 
truly  melodious.  It  seems  to  the  writer  that  at  the  present  day  the 
import  of  the  word  counterpoint  is  largely  historical.  Certainly  the 
rules  still  in  vogue  in  the  majority  of  the  books  on  counterpoint  are 
those  which  were  practised  when  music  was  under  the  influence 
of  the  old  modal  system,  was  written  almost  exclusively  for  voices, 
and  long  before  the  principles  of  rhythm  and  of  tonality,  so  deeply 
implanted  in  our  modern  instrumental  music,  had  come  into  exist- 
ence at  all.  Moreover  in  these  textbooks  there  is  little  to  stimu- 
late the  imagination  of  the  student  or  to  develop  a  broad 
musical  judgment.  The  subjects  given,  with  their  heterogeneous 
and  unrhythmic  collection  of  whole  notes,  seem  at  best  merely  to 
furnish  opportunities  for  the  acquisition  of  a  rudimentary  power 
of  selection.  But  this  selecting  and  grouping  of  the  various 
chord-factors  in  the  most  effective  way  have  already  been  taught 
the  student  during  his  course  in  harmony,  —  when  that  subject  has 
been  properly  taught,  that  is,  without  a  servile  dependence  upon 
the  figured-bass  system.  In  fact,  whoeve'r  has  been  writing  free 
exercises  in  harmony  under  competent  instruction  has  also  been 
writing  counterpoint  of  a  certain  kind;  that  is,  he  has  been  mak- 
ing the  separate  voices  as  varied  and  melodious  as  possible.! 
Every  one  will  recognize  the  great  discrepancy  in  style  between 
the  counterpoint  of  the  textbook  and  that  of  a  Mozart  String 
Quartet,  a  Beethoven  Symphony,  or  even  the  contrapuntal  accom- 
paniment of  a  Franz  song.  There  must  of  necessity  be  some  differ- 
ence ;  one  is  an  exercise  for  the  young  student ,  the  other  the  work 
of  mature  genius.  Nevertheless  the  difference  should  be  one 
rather  of  degree  than  actually  of  kind.  In  both  exercise  and  work 
of  creative  imagination  should  be  found  the  broad  principles  of 
all  musical  art;  there  should  be  life,  spontaneity  and  freedom, 
and  all  the  voices,  whenever  possible,  should  say  something, 
except  where  a  confessedly  homophonic  J  style  is  being  used . 
In  music,  of  all  arts,  "  the  letter  killeth,  but  the  spirit  giveth  life." 
Hence  the  writer  has  no  sympathy  with  the  arbitrary  division  of 
counterpoint  into  two  classes,  strict  and  free. 

*  That  is,  music  in  many  independent  parts. 

t  Since  the  time  of  J.  S.  Bach  there  is  no  reason  for  considering  harmony  and 
counterpoint  as  separate  and  unconnected  subjects;  each  is  indissolubly  bound 
«p  with  the  other. 

\  That  is,  where  there  is  one  chief  melody,  and  the  other  voices  are  frankly  sub- 
ordinate, furnishing  merely  an  accompaniment. 


vi  Preface 

For  the  last  two  hundred  years  all  contrapuntal  writing  which 
has  had  any  intrinsic  musical  value  has  been  free,  save  those  occa- 
sional instances  in  which  the  composer  has  written  in  the  old  style 
as  a  historical  tour  de  force.  Those,  however,  who  approve  of  the 
above  classification  claim  that  it  is  as  necessary  for  the  young  com- 
poser to  submit  himself  rigorously  to  the  strict  style  before  he 
attempts  the  free,  as  it  is  for  the  would-be  pianist  to  practise  five- 
finger  exercises  before  he  undertakes  the  works  of  Beethoven, 
Chopin  and  others.  This,  however,  is  a  fallacious  form  of  argu- 
ment, for  the  cases  are  really  not  parallel.  The  pianist  is  training 
himself  to  perform  and  to  interpret  adequately  works  already  writ- 
ten. The  young  musician  is  training  himself  to  express  clearly 
whatever  his  fancy  may  suggest,  and  to  make  intelligent  and 
inspiring  use  of  the  manifold  riches  of  harmony.  At  first  his  style 
is  naturally  simple  before  it  becomes  varied  and  complex,  but 
nothing  is  gained  by  keeping  him  for  months  in  the  so-called 
strict  style,  where  only  triads  are  allowed,  and  no  six- four  chords, 
and  no  modulations,  etc.,  and  then  suddenly  telling  him  that  now 
he  is  to  write  free  counterpoint,  that  in  which  he  is  to  do  what- 
ever he  likes,  without  any  previous  practice  in  adapting  means  to 
ends.  Rather  from  the  outset  the  student  should  be  led  on 
gradually  to  make  original  use  of  as  broad  a  harmonic  scheme  as 
possible.  Without  foregoing  the  technical  training  gained  by 
the  observance  of  certain  fundamental  laws,  this  book  is  meant 
to  embody  a  plea  for  the  spirit  of  modern  counterpoint  or 
free  part -writing ;  that  is,  the  combination  of  rhythmical,  freely 
moving  melodies  within  the  limits  of  concordant  harmonies. 
As  in  its  general  style  all  part- writing  must  be  largely  "  vocal," 
the  first  part  of  this  book  is  devoted  to  writing  for  voices  "  a 
capella."  This  is  the  most  natural  as  well  as  the  simplest  approach 
to  the  subject.  But  as  all  music  must  be  outwardly  performed  * 
and  as  each  instrument  —  the  human  voice,  the  violin,  the  piano- 
forte, the  organ  —  has  its  special  characteristics  of  limitation  or 
advantage,  music  must  always  be  written  with  a  clear  conception 
of  the  nature  of  the  medium  through  which  it  is  to  be  presented ; 
for  example,  that  which  is  possible  with  strings  or  pianoforte  might 
or  might  not  be  feasible  for  voices.  The  counterpoint  of  a  Bach 
Prelude  for  pianoforte  is  not  of  the  same  nature  as  the  counter- 
point of  a  Beethoven  string  quartet.  In  no  respect  is  the  student 
more  likely  to  go  astray  than  in  his  failure  to  realize  the  special 
idiom  of  the  instrument  for  which  he  may  be  writing.  The 
second  portion  of  the  book,  therefore,  deals  in  writing  for  strings, 
concluding  with  some  general  suggestions  with  reference  to  free 
composition  for  the  pianoforte. 

Attention  is  particularly  called  to  the  fact  that  very  few  rules 
are  given  as  to  "  what  not  to  do  "  in  music.  Almost  anything  can 
be  done  at  some  time  or  other  (for  music  is  not  a  matter  of  morals) , 
when  for  the  sake  of  special  effect  a  departure  is  made  from  the 
normal  rules.  What  is  needed  is  a  well-trained  instinct  as  to 
whether  any  given  effect  justifies  itself.  In  no  way  is  this  power 
gained  so  surely  or  quickly  as  by  a  thorough  study  of  the  composi- 
tions of  the  great  masters,  Bach,  Handel,  Haydn,  Mozart,  Beethoven, 
and  others.  No  one  ever  becomes  a  geologist  merely  by  the  study 
of  books  on  the  subject  but  rather  by  going  out  into  the  fields  and 

*  The  written  notes  are  merely  dead  symbols  until  the  air  is  put  into  vibration 
in  accordance  with  them. 


Preface  mi 

examining  the  works  of  nature  at  first  hand.  Likewise  in  music, 
example  is  much  better  than  precept.  Very  few  prohibitive  rules 
will  be  found  in  this  book,  and  as  far  as  possible  every  suggestion 
and  recommendation  is  confirmed  and  illustrated  by  an  example 
from  some  standard  composer.  Particular  attention  has  been 
paid  to  rhythm  and  to  the  underlying  principles  of  melody  forma- 
tion, and  the  Canti  Fermi  have  been  carefully  selected  with  refer- 
ence to  their  melodic  possibilities.  Too  often  it  happens  that  the 
subjects  given  for  treatment  in  the  various  textbooks  are  in  them- 
selves not  melodious;  they  are  either  unrhythmic  or  unsugges- 
tive,  and  far  too  much  in  the  nature  of  musical  conundrums,  In 
fact,  it  would  often  be  very  difficult  to  decide  whether  they  were 
iambic  or  trochaic.  Surely  an  easily  recognized  rhythm  in  a  given 
subject  is  an  absolute  necessity  (many  effects,  for  instance,  being 
possible  on  a  weak  beat  which  on  a  strong  beat  are  questionable) . 
Accordingly,  with  the  broad  definition  before  us  that  counterpoint 
is  the  "  art  of  inventing  melodies,"  it  is  only  fair  to  the  student 
that  the  character  of  the  Canto  Fermo  should  not  make  a  flowing 
and  melodious  contrapuntal  treatment  impossible. 

As  soon  as  the  first  principles  of  contrapuntal  style  are  under- 
stood, much  attention  is  paid  to  original  work,  for  in  the  study 
of  counterpoint  the  chief  object  is  to  increase  the  power  of 
musical  expression.  The  student  is  thrown  entirely  upon,  his  own 
resources,  and  whether  he  has  much  or  little  to  say  he  must  practise 
till  he  can  express  his  musical  thoughts  with  clearness  and  convic- 
tion. The  value  of  the  creative  spirit  should  be  kept  constantly 
in  mind.  Let  both  teacher  and  student,  then,  cherish  and  cultivate 
the  desire  to  give  outward  utterance  to  some  musical  thought. 
This  may  seem  like  a  very  advanced  standpoint  for  the  average 
student,  yet  the  writer  is  convinced  that  most  of  the  textbooks  on 
harmony  and  counterpoint  make  a  great  mistake  in  laying  so 
much  stress  on  "  what  may  not  be  done  "  rather  than  adopting  a 
definite  policy  of  encouragement.  Gradually  a  large  part  of  the 
student's  energy  is  taken  up  in  obeying  long  lists  of  rules  more 
or  less  arbitrary,  and  his  natural  instinct  is  thereby  deadened.  By 
this  criticism  no  encouragement  is  meant  to  be  offered  for  shirking 
strict  methodical  discipline.  An  earnest  worker  soon  sees  that  the 
truest  command  of  freedom  from  normal  procedure  is  gained  by  a 
thorough  understanding  of  the  general  rule.  In  art  as  well  as  in 
ethics  there  is  a  "  perfect  law  of  liberty."  Rules,  however,  which 
are  merely  prohibitory,  have  in  general  been  avoided  in  this  book. 
Better  is  it  to  encourage  the  young  musician  to  do  something 
even  though  he  flounders  around  a  bit  at  first,  than  to  have  his 
spontaneity  checked  on  every  side  by  "  what  not  to  do."  In  fact, 
to  write  really  musical  exercises  in  accordance  with  the  restrictive 
rules  found  in  many  books  would  be  as  impossible  as  to  exercise 
freely  and  joyously  in  a  suit  of  mediaeval  armor.  The  way  in 
which  one  learns  to  handle  the  boundless  resources  of  modern  musical 
material  is  to  make  use  of  them  until  there  has  been  acquired  a 
keen  and  accurate  judgment  on  which  the  composer  can  rely. 

It  would  be  disingenuous  for  the  writer  to  claim  originality  for 
this  book.  On  the  contrary  he  has  made  a  free  use  of  the  re- 
searches and  methods  of  such  distinguished  theorists  and  teachers 
as  Dubois,  Lavignac,  Rheinberger,  Riemann,  Bussler  and  Prout. 
The  method  of  teaching  outlined  is  that  followed  in  the  best  foreign 
conservatories  and  successfully  used  in  Harvard  LTniversity,  — 
that  is,  plenty  of  free,  original  work  and  copious  examples  from 


viii  Preface 

the  works  of  the  great  composers.  In  a  sense  any  book  on  counter- 
point is  an  anomaly.  From  books  one  can  as  well  learn  how  to 
write  counterpoint  as  to  make  a  water-color.  The  only  way  to 
gain  growth  in  fancy  and  facility  in  expression  is  to  write  music. 
Towards  that  end  it  is  hoped  that  the  suggestions  in  this  book 
may  be  of  value. 

WALTER  R.  SPALDING. 


TABLE  OF  CONTENTS 


PAGE 

PREFACE  ....          .          .  .  .      vii 

CHAPTER 

I.  GENERAL    LAWS    OF    HARMONIC    AND    MELODIC 

PROGRESSION i 

II.  TWO-PART     COUNTERPOINT  —  FIRST      ORDER 

(NOTE  AGAINST  NOTE)         .  .         .         -58 

III.  TWO-PART      COUNTERPOINT  —  SECOND      ORDER 

(TWO    NOTES    AGAINST    ONE)  .  ...          67 

IV.  TWO-PART  COUNTERPOINT  —  THIRD  ORDER 
(FOUR  NOTES  AGAINST  ONE).  OTHER  RHYTH- 
MIC COMBINATIONS  ...  .  .  .86 

V.  SYNCOPATED  COUNTERPOINT.  RHYTHMIC  EM- 
BELLISHMENTS .  .  .  .  .  .  .109 

VI.  TWO-PART  COUNTERPOINT  IN  THE  FLORID  STYLE. 

VARIED  MELODIC  DESIGNS        .         .         .         .119 

VII.  THREE-PART  COUNTERPOINT,  INTRODUCING 
VARIOUS  COMBINATIONS  OF  THE  PRECEDING 
ORDERS.  SIMPLE  TRIOS  FOR  STRINGS  AND 
FOR  ORGAN  .  .  .  .  .  .  .128 

VIII.   FOUR-PART     WRITING  —  FOR    VOICES,     FOR 

STRINGS  AND  FOR  ORGAN  .         .         .         .154 

IX.  DOUBLE  COUNTERPOINT;  PIANOFORTE  INVEN- 
TIONS ........  187 

X.  IMITATIVE  COUNTERPOINT    .         .         .         .         -215 

XI.   FREE  WRITING  FOR  PIANOFORTE.     HOMOPHONIC 

STYLE        ........     222 

XII.  WRITING  FOR  STRING  QUARTET  ....     236 

XIII.  SUPPLEMENTARY  EXERCISES  IN  VARIOUS  STYLES 
FOR  VOICES  AND  FOR  STRINGS.  ACCOUNT  OF 
THE  ^EOLIAN,  DORIAN  AND  PHRYGIAN  MODES. 
LIST  OF  COMPOSITIONS  RECOMMENDED  FOR 
ANALYTICAL  STUDY  ......  248 


TONAL  COUNTERPOINT 


STUDIES  IN  PART-WRITING 


CHAPTER  I 
General  Laws  of  Harmonic  and  Melodic  Progression 

§i.  The  first  requisite  for  the  student  who  has  just  fin- 
ished the  study  of  harmony  is  the  power  to  look  at  music 
horizontally.  Heretofore  he  has  either  built  up  harmo- 
nies on  a  given  bass,  or  placed  harmonies  below  a  melody 
in  the  soprano.  To  form  correct  chords  and  to  connect 
them  in  a  grammatical*  and  fairly  agreeable  way  has 
taken  most  of  his  attention.  Henceforth  the  melodic 
interest  of  each  voice,  individually  and  in  its  relation  to 
the  other  voices,  is  chiefly  to  be  considered.  The  eye  must 
follow  each  part  throughout  its  range,  and  the  endeavor 
must  be  directed  toward  the  formation  of  a  good  flow- 
ing melody. 

§2.  A  second  point  of  difference  between  the  study  of 
harmony  and  counterpoint  is  this:  that  whereas  the  mel- 
ody has  heretofore  always  been  either  in  the  bass  or  in 
the  soprano,  nothing  is  more  common  in  free  part-writing 
than  to  find  the  melody  in  one  of  the  inner  voices. 
When  the  chief  melody  is  so  placed,  there  is  implied  in 
four-part  writing  the  power  to  invent  a  bass  which  shall 
be  good  both  harmonically  and  melodically,  and  a  melo- 
dious, interesting  soprano,  besides  one  inner  part.  At 
the  same  time  these  voices  must  be  so  planned  that  the 
harmonic  background,  outlined  by  the  notes  sounded  to- 
gether on  the  strong  beats,  shall  be  natural  and  satisfac- 
tory. In  all  polyphonic  music  (and  by  polyphonic  music 

*  By  the  term  "  grammatical  "  applied  to  music  we  would  indicate  the  funda- 
mental laws  of  chord  connection;  that  is,  voices  shall  not  move  in  parallel  perfect 
fifths  or  in  parallel  octaves;  dissonant  chords  must  be  resolved  in  accordance 
with  their  tendency  tones,  —  sevenths  resolving  downward ;  augmented  intervals 
expanding  and  diminished  contracting.  Cross  relations  should  seldom  appear 
between  the  voices,  etc. 


Copyright,  fQO4,  by  Arthur  P.  Schmidt 


Tonal  Counterpoint 


is  meant  that  in  which  each  voice  has  independent  melodic 
interest  and  importance),  these  two  aspects  have  to  be 
borne  constantly  in  mind,  —  the  vertical,  representing 
the  harmonic  aspect;  and  the  horizontal,  the  contrapuntal 
and  melodic. 

§3.  In  modern  part  -writing  it  is  taken  for  granted  that 
the  harmony  shall  be  good;  the  attention  is  given  to  mak- 
ing the  different  voices  express  as  much  as  possible.  Often, 
however,  the  student,  when  he  begins  the  study  of  part- 
writing  and  has  to  depend  entirely  on  his  own  ingenuity 
and  artistic  judgment,  finds  that  his  technical  knowledge 
of  harmony  is  inadequate.  He  tries  diligently  to  write 
good  counterpoint  on  bad  harmony  —  an  impossibility. 
Let  us,  therefore,  speak  of  certain  chords  and  harmonic 
combinations  which  are  likely  to  trouble  the  beginner, 
and  later  inquire  into  the  nature  of  melody,  that  the  stu- 
dent may  see  what  are  the  characteristics  of  a  good  mel- 
odic motion  in  the  different  parts. 

§4.  At  first  we  center  our  attention  entirely  on  triads 
or  combinations  of  three  tones.  No  matter  how  elabo- 
rate our  writing  may  become,  well-connected  triads  are 
always  the  element  which  gives  strength  and  firmness  to 
the  harmonic  structure. 

§5.  The  fundamental  Harmonic  Progressions,  that  is, 
the  ones  which  clearly  establish  the  given  tonality  and  are 
smoothest,  are  those  in  which  the  bass  moves  a  fifth  up 
or  down;  for  example,  I,  V;  I,  IV;  n,  vi;  in,  vi;  n,  V;  as 
a  fifth  is  the  inversion  of  a  fourth,  the  student  will  readily 
understand  that  a  fifth  upwards  is  equivalent  to  a  fourth 
downwards  and  vice  versa.  In  like  manner  a  sixth  is  the 
inversion  of  a  third,  and  a  second  of  a  seventh.  Worked 
out  in  four  parts  these  progressions  will  be  the  well-known 
ones  which  the  student  has  used  again  and  again  in  his 
studies  in  harmony.  In  counterpoint  these  combina- 
tions are  by  no  means  thrown  aside;  they  are  only  ampli- 
fied in  various  ways,  and  more  attention  is  paid  to  the 
melodic  progression  of  the  voices. 


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N.  B. 


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General  Laws  of  Progression 


3 


N.  B.  —  In    the    connection   n,  V,  it  is  almost  always  / 
better,  when  the  bass  ascends,  to  make  the  other  voices  / 
move  downwards  in  contrary  motion.     This  secures  mel^J 
odic  movement  for  the  soprano,  and  questionable  hidden 
octaves  are  avoided;  for  example, 

(a)  good        (b)  less  good    (c)   bad 


l-A 

. 

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c  r 

n    V 


ii    V 


ii    V 


These  octaves  are  thorouglily  bad  only  when  they  are  in 
the  outer  voices  as  at  (c)  ;  occasionally  it  is  necessary  to 
use  the  combination  shown  in  example  (6),  though,  when- 
ever it  is  possible,  the  effect  at  (a)  is  decidedly  the  smooth- 
est. When  we  come  to  the  consideration  of  the  minor 
mode,  the  student  will  see  the  importance  of  this  recom- 
mendation. Here,  with  the  normal  leading  of  the  parts, 
it  is  almost  always  bad  to  hold  the  common  tone  on  ac- 
count of  the  unmelodic  augmented  second  which  is  caused 
thereby,  example  (a)  : 


(a)   bad 

(b) 

good      (c)    best 

-1  — 

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In  free  writing  for  strings,  or  occasionally  for  voices, 
example  (b)  with  the  diminished  fifth  in  the  tenor  would 
be  of  perfectly  good  effect,  but  the  best  and  most  natural 
combination  is  that  shown  at  (c). 

§6.  Less  usual,  in  general,  are  those  progressions  in 
which  the  bass  moves  a  third  up  or  down;  n,  IV;  in,  V; 
vi,  I;  etc.  The  combinations  in  which  the  subordinate 
triad  comes  first,  though  possible,  should  not  be  used  fre- 
quently; for  example, 


Tonal  Counterpoint 


n    IV 


The  reverse  progression,  however,  in  which  the  principal 
triad  comes  first,  is  always  good  and  of  frequent  occur- 
rence; for  example, 


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The  student  will  note  that  this  combination  is  essentially 
the  progression  from  a  triad  to  its  relative  minor. 

§7.  Least  common,  as  far  as  natural  relationship  is 
concerned,  though  capable  of  being  used  with  good  effect, 
are  those  combinations  in  which  the  bass  moves  step  wise, 
that  is,  a  second  up  or  down,  —  I,  n;  V,  vi;  vi,  V;  IV,  V;  V, 
IV.  In  the  use  of  this  progression  the  student  must  strongly 
impress  upon  himself  that  triads  situated  on  adjoining 
degrees,  when  they  are  both  used  in  the  fundamental  posi- 
tion, have  no  inherent  connection,  that  is,  no  common 
tone,  and  that  in  such  cases  the  invariable  use  of  contrary 
motion  is  the  only  means  of  avoiding  gross  mistakes  in 
rudimentary  grammar.  Some  of  the  possible  combina- 
tions of  these  adjacent  triads  would  be  the  following: 


(a) 


N.B.  seldom 

good     possible       used 


ff 


J.~ 


A 


J^ 


m 


I     it         I    n      V    vi       vi    V      IV  V      IV  V       V  IV      V  IV      V    IV 

At   (a)   note  the  doubled  third  in  the  triad  on  the  sixth 
degree  in  the  well-known  progression  from  V  to  vi.     Here 


General  Laws  of  Progression  5 

again  it  is  advantageous  for  the  student  to  think  of  the 
voices  as  generally  progressing  along  these  lines,  for, 
though  the  following  combination  is  natural  in  the  major 
mode,  and  of  perfectly  good  effect  (with  leading  tone 
descending  and  with  doubled  root}, 


V    vi 


the    corresponding    combination    in    the    minor    mode   is 
entirely  false;  for  example,  in  A  minor, 


good 


v  vi 

§8.  To  the  correct  use  of  the  triads  V  and  IV,  when  both 
are  in  the  fundamental  position,  the  student  will  have  to 
give  much  attention.  In  fact,  beginners  make  more  mis- 
takes in  the  connection  of  these  two  triads  than  with  all 
the  rest  taken  together.  The  chief  points  to  be  borne  in 
mind  are  as  follows:  First,  it  is  much  more  natural  and 
common  to  progress  from  IV  to  V  (that  is,  from  the  under 
or  subdominant  to  the  upper  or  main  dominant)  than  vice 
versa.  Second,  the  dominant  and  subdominant  triads 
have  no  inherent  connection,  that  is,  no  common  tone; 
they  merely  have  the  secondary  connection  of  referring 
to  the  same  common  tonic.  In  fact,  when  this  combina- 
tion is  played,  a  distinct  feeling  of  disfunction  is  apparent, 

C  majot 


V     IV 


Tonal  Counterpoint 


which  would  be  much  less,  even  with  the  faulty  parallel 
motion,  were  the  combination  either 


G  major 


F  maior 


°r 


ii    I 


Third,  the  progression  from  V  to  IV  does  not  arouse  a  defi- 
nite feeling  of  tonality.  We  often  find  in  the  old  Church 
Composers  phrases  like  the  following : 


PALESTRINA.    "  Stabat  Mater" 


(V  IV) 
(V  IV) 

and  while  these  effects  were  perfectly  valid  in  the  days 
of  the  ecclesiastical  modes,  they  are  rather  vague  (except 
for  special  effect)  from  the  modern  standpoint  of  definite 
tonality.  This  tonal  uncertainty  of  V  and  IV  is  caused  by 
the  fact  that  the  dominant  progresses  so  much  more  natu- 
rally to  the  tonic  triad  with  which  it  has  a  tone  in  common 
than  to  the  subdominant,  that  the  progression  V,  IV,  when 
the  subdominant  comes  on  the  strong  beat,  has  practi- 
cally the  effect  of  breaking  away  from  the  key.  This  pro- 
gression therefore  is  to  be  used  only  when,  for  esthetic 
and  dramatic  reasons,  such  an  abrupt  transition  is  desir- 
able; for  example. 


3cf=f 


A 


~M 
5^? 


il 


instead  of 


ffc    rj    <d 

tP  f9  r 
1  J 

*):    [      ['  : 

0 

0— 

-Vf 

VI      V          IV  vi      V          I 

(a)  (b)  (c)   rare 


[#= 

I  j  A  1 

i  j  j  • 

5 

p  . 
J  ^ 

-H- 

-t—  i- 

General  Laws  of  Progression 


7 


Long  usage  has  sanctioned  the  combinations  shown  at 
examples  (a)  and  (b),  and  they  may  be  employed  with 
good  effect;  for  example, 


P^=I 

S1-  p  \- 

f  r 

-*— 

r 

-r- 

fi 

—  e  — 

,1  J 

. 

y 

4 

j  . 

j 

I    J 
g    A 

•**• 

*)'  *f 

=4 

—  «*  — 

N 

—  «  — 

IV 


IV 


Example  (c),  however,  with  the  third  of  the  dominant  in 
the  upper  voice  should  be  used  but  rarely.  For  if  V 
and  IV  are  grouped  in  this  way 


the  interval  of  the  augmented  fourth  (or  so-called  "  tri- 
tone,"  three  whole  tones)  is  plainly  heard  between  the 
outer  voices,  and  also  between  soprano  and  tenor.  This 
"  false  relation  of  the  tritone  "  may  occur  also  between 
in  and  IV;  for  example. 


(jh  *Mi||»3£)i 

V  /    ^    V<  II  M'^J 

in  IV   IV  in 


Though  modern  taste  is  not  so  fastidious  in  regard  to  this 
interval  as  were  the  composers  of  the  fourteenth,  fifteenth 
and  sixteenth  centuries,  with  whom  it  rejoiced  in  the  name 
"  Diabolus  in  Musica,"  nevertheless  in  pure  part-writing 
for  voices  it  must  be  used  with  great  care.  It  is  not,  how- 
ever, the  presence  of  the  two  notes  f  and  b  in  consecutive 
chords  which  causes  offense,  but  rather  the  questionable 
progression  of  roots.  For  it  is  entirely  possible  to  use 
these  same  two  notes  f  and  b  in  combinations  where  the 
roots  of  the  triads,  instead  of  moving  by  steps,  as  hereto- 
fore, rise  or  fall  a  fourth,  and  the  effect  is  perfectly  good; 
for  example, 


Tonal  Counterpoint 


ffi  "\ 

t=it= 

=&= 

=jfi*= 

a 

a 

v> 

V 

y 

il 

IV 


ii         V 


§9.  In  actual  music,  of  course,  not  all  or  even  the  ma- 
jority of  the  triads  are  in  the  fundamental  position.  As 
soon  as  one  or  both  of  two  triads  are  in  the  first  inversion, 
the  connection  becomes  much  smoother,  and  the  differ- 
ent parts  can  move  in  a  more  cantabile  manner.  For 
instance,  with  the  following  phrase  in  the  soprano, 


it  is  by  no  means  incumbent  upon  the  student  to  limit 
himself  to  fundamental  positions  of  triads,  and  to  har- 
monize as  follows: 


i 


Here  so  many  fundamentals  in  f  succession  give  a  rigid 
effect,  and  the  use  of  the  subordinate  triads  11  and  in  rather 
weakens  the  tonality.  By  the  introduction  of  first  inver- 
sions the  phrase  may  be  treated  as  follows : 


The  chords  now  blend  together  more  naturally,  and  we 
secure  a  -flowing  diatonic  bass  melody. 


General  Laws  of  Progress-ion 


§10.  To  speak  now  in  detail  of  certain  harmonic  diffi- 
culties, —  in  the  major  mode,  barring  the  fact  that  the 
beginner  often  makes  too  much  use  of  the  subordinate* 
triads  n,  in  and  vi,  instead  of  establishing  the  tonality  by 
an  effective  grouping  of  I,  V  and  IV,  there  is  only  one 
triad  which  should  give  much  trouble, — the  diminished 
triad  on  the  leading  tone  (seventh  degree),  in  C  major, 
B,  D,  F.  The  facts  constantly  to  be  borne  in  mind  in  the 
use  of  this  chord  are  these:  First,  its  lowest  note  is  the 
leading  tone;  second,  the  interval  from  this  to  its  highest 
note  is  a  dissonance,  a  diminished  fifth.  If  we  use  this 
chord  in  its  fundamental  position,  that  is,  with  its  lowest 
note  in  the  bass  and  with  this  note  doubled,  the  dimin- 
ished fifth  is  too  prominent  and  the  effect  is  very  harsh: 
for  example, 


bad 


bad         bad 


The  chord  therefore  is  almost  never  used  in  its  fundamental 
position,  except  in  sequences,  and  even  then  it  sounds 
weak,  although  the  ear  is  diverted  by  following  out  the 
symmetrical  arrangement  of  the  parts;  for  example, 

*  This  statement  should  not  be  taken  so  literally  that  the  secondary  triads  are 
avoided  altogether.  They  may  often  be  used  with  striking  effect  in  just  the  right 
context.  The  artistic  judgment  is  to  be  cultivated,  so  that  when  these  triads  are 
introduced  the  effect  may  be  convincing;  for  example,  the  following  well-known 
phrase  from  Wagner's  "  Tannhaiiser  ": 


10 


Tonal  Counterpoint 


E.b  4  • 


Third,  the  chord  is  likewise  seldom  used  in  its  second 
inversion;  in  very  rare  cases  is  the  following  combination 
available;  for  example, 


The  student  will  occasionally,  it  is  true,  find  passages 
like  the  following: 


BACH.    Cantata 


but  it  is  quite  evident  upon  analysis  that  the  six-four 
chord  of  the  diminished  triad  is  of  no  harmonic  import, 
being  used  on  the  weak  part  of  the  second  beat.*  As  soon, 
however,  as  we  place  this  triad  in  the  first  inversion, 

*  Compare  also,  for  an  analogous  effect,  the  last  phrase  of  Dyke's  well-known 
hymn  tune,  "  Lead,  Kindly  Li<:ht." 


m 


General  Laws  of  Progression 


TI 


the  dissonance  between  the  bass  and  any  one  of  the  upper 
parts  is  entirely  removed;  for  example, 


fi*= 

(a)            (6)               (c) 
J      „       J       „       J      „ 

55 

s 

-f— 

T 

—  F— 

and  so  this  leading  tone  triad  as  a  chord  of  the  sixth  is  one 
of  the  most  common  and  effective  in  music.  Either  the 
original  third  or  the  original  fifth  is  doubled  with  equally 
good  effect;  for  example,  at  (a)  and  (6)  above  we  have  a 
doubled  third,  and  at  (c)  a  doubled  fifth.  The  following 
example  from  Handel's  "  Messiah  "  is  instructive,  as  in 
it  we  find  three  first  inversions  of  leading  tone  triads. 


In  this  passage  we  see  also  the  different  possibilities  of 
"  doubling."  At  (a)  and  (c)  the  original  third  is  doubled, 
and  at  (b)  the  original  fifth. 

§11.  With  the  growing  prevalence  of  dominant  seventh 
harmony  during  the  last  two  centuries,  the  second  inver- 
sion of  the  dominant  seventh  (the  so-called  chord  of  the 
third  and  fcnirth)  may  seem  to  the  student  richer  in  its 
effect  as  well  as  more  customary,  but  the  inversion  of  the 
simple  triad  is  often  purer  and  stronger,  especially  in  com- 
positions for  voices  "  a  capella,"  *  wherein  a  too  frequent 
use  of  the  inversions  of  the  dominant  seventh  chord  has 
a  rather  cloying  effect.  This  the  student  can  verify  for 
himself  by  a  comparison  between  the  following  well-known 
cadences : 

*  By  "  a  capella  "  is  meant  vocal  music  without  accompaniment. 


12 


Tonal  Counterpoint 


(a) 


(b)        or 


sH-t 

j):ij  fj't 

, 

« 

f 

J 

4 

^ 

VI 

I« 

=£ 
VII« 

y; 

At  (a)  and  (6)  the  skips  in  the  tenor  are  always  particu- 
larly effective  with  voices.* 

§12.  The  mediant  chord  (that  is,  the  triad  on  the  third 
degree)  also  requires  special  care  for  its  proper  use.  At 
first  it  will  be  wise  for  the  student  to  use  this  chord  very 
seldom  in  the  fundamental  position,  for  it  is  one  of  the 
most  indefinite  of  the  secondary  triads. 


in    ii  vi    in    ii    vi    in  IV  I 


Passages  like  the  above,  however  good  and  effective  they 
may  have  been  in  the  modal,  ecclesiastical  style,  should 
be  employed  judiciously  in  modern  music,  and  introduced 

*  It  is  understood,  of  course,  that  the  two  chords  in  question  are  closely  allied. 
In  fact,  the  diminished  triad  on  the  leading  tone  has  no  satisfactory  individuality 
at  all,  any  more  than  any  triad  which  has  a  diminished  or  an  augmented  fifth.  It 
is  merely  an  incomplete  dominant  seventh  chord  with  the  generator  or  ground 
tone  omitted;  for  example, 


In  passing  we  may  point  out  that  the  same  chord  when  found  on  the  second  degree 
of  the  minor  mode  is  closely  related  to  the  chord  of  the  seventh  on  the  leading  tone 
(the  so-called  diminished  seventh  chord),  which  in  its  turn  is  nothing  but  an  in- 
complete dominant  minor  ninth  chord.  The  following  chart  will  make  this  clear: 


n«  VII*-'7  V'-1 


General  Laws  of  Progression 


only  when  a  vague,  mysterious  effect  is  desired.*  After 
the  tonality  of  a  phrase  has  been  established,  the  mediant 
triad  may  often  be  introduced,  especially  in  connection 
with  one  of  the  other  secondary  triads,  vi  or  n ;  for  example, 


r 


i 


rr 


rr 


? 

I      I     V   vi    in    vi    V      I 

In  general,  however,  the  mediant  triad  is  most  effective 
in  its  first  inversion,  that  is,  with  the  dominant  of  the  key 
in  the  bass,  and  is  used  either  in  connection  with  other 
chords  of  the  sixth  or  with  subsequent  dominant  harmony. 
The  following  chart  exemplifies  the  most  normal  and 
useful  combinations,  and  if  the  student  will  play  it  over 
and  commit  it  to  memory  he  will  have  very  little  trouble. 

possi-    possi-     very       very    very  good ; 
good      good    not  bad      ble         ble       good       Rood    often  used          weak 


1 

-L 

-J-U 

J 

r 

| 

1 

I 

J 

J: 

i 

LJ4 

I 

6 
J 

to 
o 

J 

6 

4 

£> 

o 

, 

j 

|t 

U=J 

—  11 

J  —  LJ 

-1—  1 

LL 

i 

in  vi  in  vi  in  vi  in  ii  in  vi i«  in  ii  in  IV  in  V   I   in  vi 

The  last  measure  of  the  above  chart  illustrates  a  combi- 
nation the  student  may  be  tempted  to  use ;  it  should  gen- 
erally, however,  be  avoided,  for  the  two  secondary  triads 
used  together,  each  in  the  first  inversion,  and  with  a  leap 
in  the  bass,  give  a  very  weak  progression.  To  sum  up 

*  For  a  beautiful  use  of  secondary  triads  see  the  following  passage  from  Elgar's 
"  Dream  of  Gerontius  "• 


/4  Tonal  Counterpoint 

the  matter  of  the  last  few  paragraphs,  -  -  nothing  con- 
duces more  to  a  well-established  tonality  (and  modern 
music  in  general  presupposes  a  definite  key  system)  than 
the  realization  that  the  triads  on  the  second,  third  and 
sixth  degrees  of  the  scale  are  subordinate  and  secondary 
to  those  on  the  fourth,  fifth  and  first,  respectively. 

§13.  As  the  triads  in  the  minor  mode  are  more  varied 
than  those  in  the  major,  that  is,  two  diminished  triads  on 
the  second  and  seventh  degrees  (11°  and  vn°)  to  one  in  the 
major  (vn°)  and  an  entirely  new  one  the  augmented  triad 
on  the  third  degree  (III')»  so  greater  care  is  needed  in  the 
use  of  each  of  them,  and  in  their  interconnection  certain 
principles  have  to  be  rigorously  observed.  The  first  strik- 
ing fact  is  that  the  diminished  triad  B,  D,  F,  may  be  used 
with  good  effect  in  its  fundamental  position  in  the  key 
of  A  minor,  whereas  the  same  triad  in  C  major  was  found 
to  be  very  harsh  in  sound,  and  difficult  to  connect  with 
other  chords.  The  reason  is,  of  course,  that  B,  the  low- 
est note,  is  no  longer  the  leading  tone.  The  student  may  see 
this  very  clearly  for  himself  if  he  will  first  play  several 
C's  in  octaves  with  a  strong,  firm  touch;  that  is, 


and  then  strike 
this  chord: 


He  will  instantly  feel  how  harsh  this  chord  is  in  itself,  and 
how  difficult  to  be  combined  effectively  with  other  chords. 
Now,  after  a  pause,  let  him  play  several  A's  in  the  same 
manner,  and  follow,  them  by  the  same  chord.  Though 
the  chord  is  still  felt  to  be  a  discord,  it  is  not  so  harsh,  and 
smooth  combinations  will  at  once  suggest  themselves; 
for  example, 


")-j-| 

-j— 

:jz=b 

^= 

| 

^r 

=F=|=| 

•4 

4 

f 

"fM 

i 

t 

3 

^ 
J: 

.1 

J- 

j 

rT 
JLJ 

•4*- 

1          *• 

N 

—  ^ 

-jHJ- 

K 

rt 

a: 


General  Laws  of  Progression 


At  *  note  carefully  the  chord  in  question  with  doubled  B. 
This  shows  how  powerful  with  us  in  modern  times  is 
the  effect  of  tonality,  or  the  principle  by  which  all  chords 
in  a  key  are  felt  to  bear  a  fixed  and  definite  relationship 
to  a  common  center,  or  tonic.  This  diminished  triad  on 
the  second  degree  of  the  minor  mode  is,  to  be  sure,  often 
used  so  as  to  give  prominence  to  its  intrinsic  dissonant 
effect.  In  such  cases  the  progression  is  generally  along  the 
usual  lines  of  all  primary  discords;  the  bass  ascends  a 
fourth  and  the  triad  resolves  to  the  dominant, —  that  is,  the 
chord  really  returns  to  its  origin;  for  example, 

i=£ 


no    V" 


Instructive  examples  are  cited  from  Bach,  from  Mendels- 
sohn and  from  Wagner. 


Toccata  in  F 


"  St.  Paul  " 


In  the  first  two  of  these  examples,  between  11°  and  V 
passing  notes  are  inserted  on  the  weak  beats,  but  they  in 
nowise  disturb  the  main  lines  of  the  progression. 

'  Walkyrie,"  Hunding-Motive 

T- 


i6 


Tonal  Counterpoint 


§14.  The  triad  on  the  leading  tone  in  the  minor  mode, 
for  example,  in  A  minor  G#,  B,  D,  is  treated  in  accordance 
with  the  same  principles  of  voice-progression  and  of  doub- 
ling as  the  corresponding  triad  in  the  major  mode.  It  is 
only  fair  to  say  that  both  diminished  triads  of  the  minor 
mode  are  used  more  frequently  in  their  first  inversion. 
The  following  chart  illustrates  the  usual  and  most  natural 
combinations : 


L"  n  hi 

JJLhjJiJJi  JJ=ph 

6    6 

Tf 

6    6 

rr 

6   6 

-p-w- 

rr 

p  r 

r 
=t= 

K^I  1*  rip  i  H|  i  M  i  ±^=* 

vn«          vae           lie    I         IV    V          I 

One  very  important  point  to  be  noticed  is  that  the  normal 
leading  tone,  even  where  we  are  not  writing  exclusively 
in  the  ^olian  mode  (that  is,  in  the  old  scale  of  A  minor 
with  go;)  is  often  lowered  in  a  diatonically  descending 
bass,  and  bears  above  it  a  chord  of  the  sixth.  The  open- 
ing measures  of  Mendelssohn's  Overture  to  "  Ruy  Bias  " 
are  a  striking  illustration  of  this  point. 


(a) 


i  \ 

=^^ 

"    D 

^= 

^^^ 

t^ncr 

9^ 

-*&- 

r 

r 

1 

•«*• 

-*>• 

f 

r 

| 

P 

g^-*»  6 

".  r              ^       ^-     -z 

•X-            BACH.     Mote 

:  ^ 
,t 

Also 


^^ 


Here  in  the  first  phrase  the  bass  descends  using  the  well- 
known  form  of  the  melodic  scale.  In  the  repetition  at 
(a)  the  bass  moves  from  the  seventh  degree  downward 


General  Laws  of  Progression 


only  a  semitone,  and  a  seventh  chord  on  the 
supertonic,  that  is,  a  chromatically  altered 
chord  is  used  in  its  second  inversion.  Some- 
times in  Bach  a  corresponding  effect  is  used 
with  an  ascending  bass  but  only  in  progressions 
where  the  seventh  degree  is  a  passing  note  —  a  point  to  be 
explained  later ;  for  example , 


rr 

j. 


§15.  The  triad  on  the  third  degree  in  the  minor  mode, 
the  mediant,  is  liable  to  give  much  trouble  to  young  stu- 
dents. This  triad  in  its  fundamental  position,  c,  e,  g# 
in  the  key  of  A  minor  for  instance,  is  a  triad  with  an  aug- 
mented fifth ;  hence  a  harsh  discord  in  itself  and  difficult 
to  be  connected  with  other  triads  in  the  key.  As  a  matter 
of  fact,  if  the  student  will  play  through  and  analyze  sev- 
eral well-known  movements  in  the  minor  mode  (for 
example,  several  of  Beethoven's  Pianoforte  Sonatas  and 
of  Bach's  Preludes  and  Fugues),  he  will  assure  himself  that 
this  triad  is  almost  never  used  in  the  fundamental  position 
in  a  passage  strictly  in  the  minor  mode.  The  student,  to 
be  sure,  sees  it  somewhere  or  other,  every  day  of  his  life, 
but  if  he  will  examine  these  places  it  will  be  evident  that, 
in  the  great  majority  of  cases,  the  triad  c,  e,  g#  is  an  altered 
triad  with  a  raised  fifth  (derived  from  c,  e,  g),  and  that 
the  tonality  is  C  major,  F  major  or  G  major;  that  is,  the 
triad  is  an  altered  tonic,  dominant,  or  subdominant^ 
When  this  triad  is  used  in  the  minor  mode,  it  is  almost 
invariably  in  the  first  inversion;  that  is,  with  the  dominant 
of  the  key  in  the  bass,  and  even  now  and  then  as  a  chord 
of  the  sixth  and  fourth;  for  example,  the  opening  meas- 
ures of  the  eighteenth  Prelude  from  the  first  book  of  the 
"  Well-Tempered  Clavichord." 


X      etc. 


i8 


Tonal  Counterpoint 


This  beautiful  and  instructive  passage  will 

repay  careful  examination.       The  chord  in 

question  is  the  mediant  triad  in  g#  minor. 

In  the  first  measure  we  see  it  used  in  the 

second   inversion    as  a   passing   chord,   and  in   the    next 

in  the  usual  way  as  a  chord  of  the  sixth.     In  fact,  the 

effect  of  the  dominant  in  the  bass  is  so  strong  that  this 

triad  in  its  first  inversion  is  generally  used  in  a  group  of 

dominant  harmony  to  introduce  some  more  or  less  final 

cadential  effect;  for  example, 


is 


k\,  M    : 
../'  g  ft 


or 


XL 


tt 


<u 


Furthermore,  the  dominant  effect  of  the  augmented  triad 
when  in  its  first  inversion  is  so  strong  that  it  may  proceed 
at  once  to  the  tonic  (with  an  entire  ellipsis  of  the  domi- 
nant triad  itself)  and  the  effect  will  be  that  of  a  perfectly 
satisfactory  cadence;  for  example,* 


DVORAK.    "  Stabat  Mater' 


fea 


^ 


fr 


r 


rr 


*  Some  theorists  call  the  root  of  this  chord  the  third  of  the  original  combina- 
tion, identical  with  the  dominant  of  the  key  in  question,  and  in  speaking  of  the 


General  Laws  of  Progression 

CHOPIN.    Preludes  No.   10 


TT'^J 


MARTIN.     Hymn  Tune 


,1.1,  4  J  1 

J-  . 

I 

FrN 

9?  *  Lr 

-f  —  F— 

h 

i-  ; 

s 

H= 
J. 

I'  ^   S    1       1 

a 

= 

When  the  mediant  triad  is  used  in  the  fundamental  posi- 
tion in  a  passage  strictly  in  the  minor  mode,  its  resolution 

triad  c,  e,  git  on  the  third  degree  of  A  minor  would  refer  to  e  as  the  root  and  call 
the  c  a  thirteenth ;  for  example. 


The  writer,  however,  is  not  in  sympathy  with  the  tendency  to  account  for  unusual 
harmonic  effects  by  the  assumption  of  elaborate  chord-formations  such  as  elevenths 
and  thirteenths.  In  the  first  place,  since  harmony  is  based  on  an  underlying  four- 
part  structure,  too  many  of  the  vital  factors  have  to  be  omitted  for  the  chords  to  be 
available  for  practical  use.  In  modern  music,  to  be  sure,  in  five-  and  six-part  writing 
the  harmony  often  moves  in  combinations  of  seventh  and  ninth  chords,  but  with 
reference  to  the  normal  harmonic  structure  the  statement  is  valid.  See  the  follow- 
ing passage  from  a  prelude  of  Cesar  Franck : 

Allegro  moderato  e  maestoso 


20 


Tonal  Counterpoint 


is  analogous  to  that  of  the  triad  on  the  second  degree ;  that 
is,  the  bass  ascends  a  fourth  and  we  reach  the  triad  on 
the  sixth  degree;  for  example, 


III1  VI 


This  passage,*  so  far  as  purity  of  part -motion  and  gram- 
matical connection  are  concerned,  is  perfectly  valid;  if  the 


and  further  on , 


Secondly,  all  such  effects,  instead  of  being  called  incomplete  chords  of  the  eleventh 
and  of  the  thirteenth,  can  be  explained  in  a  far  more  simple  and  natural  way  by 
referring  to  Suspensions,  Appoggiaturas,  Passing  notes, Ellipses  of  chords  of  resolu- 
tion. Pedal  points,  Anticipations  and  Retardations, — processes  of  harmonic  free- 
dom and  variety  with  which  the  student,  from  his  previous  studies,  is  doubtless 
familiar;  for  example,  at  (a)  we  find  a  triple  suspension  of  the  third,  fifth  and  of 
the  octave  from  the  root  of  a  normal  dominant  seventh  chord, 


mm 

"    *-  i' 

•J  r 

±HFF 

[  (0)111-- 

J.  J  J 

HCff 

*  Interesting  examples  of  the  treatment  of  the  mediant  triad  in  the  minor  mode 
iy  be  found  in  the  Sarabande  of  Bach's  first  French  Suite  fur  Pianoforte. 


may  be  f 


General  Laws  of  Progression 


21 


question  of  esthetic  effect  were  raised,  it  might  not  be 
considered  so  satisfactory.  At  (a)  let  the  student  ask 
himself  why  the  tenor  might  just  as  well  have  had  b 
instead  of  d. 

§16.  Though  fairly  well  grounded  in  harmony,  the  stu- 
dent cannot  be  too  often  reminded  of  the  strict  connec- 
tion always  necessary  between  triads  on  the  fifth  and  the 
sixth  degrees  in  the  minor  mode.  The  connection  be- 
tween these  chords  is  as  logical  and  strict  as  the  agreement 
between  a  verb  and  its  subject  noun  in  a  language,  and 
the  only  combinations  possible  are  such  as  these: 


>;  r-  r  ii  r 


C-  r  n  I*-  -r 


V        VI 


at  (b)  the  b  flat  in  the  melody  is  an  appoggiatura,  or  unprepared  suspension  before 
the  fifth  of  dominant  seventh  harmony. 


SCHUBERT.    Sonata,  Op. 


MENDELSSOHN.     Part-song 


wm. 


•  •    9   » 


In  this  example  we  see  tonic  and  dominant  pedal  points  with  parts  of  seventh 
chords  in  the  three  upper  voices. 


22 


Tonal  Counterpoint 


That  is,  when  triads  V  and  VI  are  used  in  the  minor  mode  < 
both  in  fundamental  position,  there  must  be  vigorous  con- 
trary motion  and  a  doubled  third  on  the  triad  of  the  sixthi 
degree.*  — \ 

§17.  No  state  of  mind  is  more  frequent  with  the  student 
than  that  of  underestimating  the  significance  of  simple 
triads.  The  amount  of  practice  necessary  to  acquire  an 
adequate  and  facile  technique  in  their  interconnection 
often  becomes  irksome  to  him.  But  as  the  human  body 
must  have  a  skeleton  of  bone,  in  like  manner  we  cannot 
compose  well-knit  music  without  triads,  even  if  we  should 
wish  to;  they  are  the  framework  of  all  our  music,  both 
simple  and  complex.  They  may  be  said  to  correspond  to 
the  primitive  colors  in  painting,  whereas  the  discords,  and 
the  more  complicated  chromatic  chords,  as  their  name 
implies,  are  used  for  subtle  effects  in  variety  of  color.  If 
all  our  chords  were  to  be  chromatic  dissonances,  or,  on 
the  other  hand,  if  we  were  never  to  use  them,  we  should 
have  in  either  case  no  contrast,  no  variety. f  The  young 
student  often  feels  that  the  dissonant  effects  are  the  diffi- 
cult ones  to  handle  and  to  resolve  effectively.  From  the 
standpoint  of  grammar  just  the  opposite  is  true.  Con- 
sider the  simple  dissonance,  g,  b,  d,  f;  we  can  hardly 
imagine  any  motion  of  the  four  notes  which  will  not  lead 
us  to  some  possible  combination,  although  from  the  stand- 
point of  artistic  effect,  some  resolutions  would  undoubt- 
edly be  preferable  in  certain  cases  to  others;  for  example, 


PS    •"- 

j^       *J  — 

—  »  —  g— 

—  8  —  8~ 

8   Vv, 

»  «ft   II 

*=£=«= 

—  u  —  w— 

M  t*  

=**= 

—  "  e  — 

"    It" 

H  0  

|    **    *t  re     || 

<  s   ^s 

§  "  t" 

*"  «  

—  8  —  J»iJ  — 

—  n  —  U— 

a    gi$. 

Consider,  however,  the  triad  e,  g,  b,  in  C  major;  this,  even 
grammatically,  can  progress  only  along  certain  lines,  and 

*  Let  the  student,  if  he  wishes,  try  to  invent  other  combinations,  and  in  so 
doing  he  will  convince  himself  that  those  cited  above  alone  are  justifiable. 

t  This  broad  statement  would  undoubtedly  need  modification  in  writing  for 
orchestra  or  pianoforte,  but  in  pure  vocal  writing,  which  we  are  at  present  con- 
sidering, it  is  undoubtedly  sound. 


General  Laws  of  Progression  23 

for  the  best  effect  to  be  secured,  it  has  to  be  treated  in  a 
very  strict  and  rather  limited  way.  So  let  the  student 
be  persuaded  to  acquire  a  sound  and  facile  technique  in 
the  treatment  of  triads.  Nothing  will  give  him  such  a 
good  foundation  for  future  development  when  he  comes 
to  free  chromatic  writing. 

§18.  The  student  is  strongly  urged  to  consult  the  com- 
prehensive charts  of  all  possible  triad  connections  in  the 
major  and  minor  modes  given  in  Prout's  "  Harmony  " 
and  in  Chadwick's  "  Harmony."  It  is  indispensable  that 
lie  should  gradually  have  these  tables  at  his  finger-ends 
as  well  as  in  his  head;  for  they  form  in  themselves  alone 
a  fundamental  system  of  diatonic  harmony  which,  if 
thoroughly  mastered,  will  be  of  the  greatest  assistance  in 
all  future  studies. 

A' '.  B.  —  The  student  is  by  no  means  expected  to  read 
over  and  assimilate  this  whole  first  chapter  before  he  be- 
gins to  write  music.  Quite  to  the  contrary,  he  is  earnestly 
recommended  to  begin  at  once  to  write  out  the  simple 
exercises  given  on  pages  48  seq.,  and  in  this  way  learn 
gradually  to  apply  the  principles  and  recommendations  set 
forth.  In  Music,  as  in  any  Art,  reading  about  the  subject  in 
the  abstract  is  of  little  avail.  Only  by  constant  methodi- 
cal practice  under  competent  supervision  may  the  stu- 
dent hope  to  acquire  an  adequate  technique  in  musical 
expression.* 

§19.  Before  we  come  to  the  practical  illustration  of 
these  general  working  principles,  it  will  be  necessary  to 
speak  somewhat  about  melody  formation,  for,  as  we  all 
know,  counterpoint,  broadly  defined,  is  the  "  Art  of 
inventing  Melodies."  In  fact,  some  teachers  when  asked 
by  the  earnest  student  who  acknowledges  this  statement, 
"  But  how  shall  I  invent  melodies?  "  simply  direct  him  to 
invent  them.  While,  to  be  sure,  this  tells  the  whole  story, 
from  the  highest  standpoint,  on  the  principle  that  the 
artist  is  "  born,  not  made,"  from  the  point  of  view  of  the 
average  student  with  musical  inclinations  it  seems  to 
the  writer  that  certain  helpful  suggestions  may  be  made. 
First,  it  must  be  recognized  that  melody  is  a  term  of  very 
broad  implication,  and  may  include  everything  from  the 
most  impassioned  operatic  Aria  to  the  simplest  Folk-song. 
In  four-part  writing  it  is  not  possible  nor  even  desir- 
able that  all  the  voices  should  be  melodies  in  the  sense  in 

*  It  is  a  well-known  fact  that  all  the  great  masters  have  begun  their  work  by 
actually  composing;  that  is,  their  skill  was  derived  from  practice  and  from  music 
itself. 


Tonal  Counterpoint 


which  we  speak  of  a  beautiful  melody  in  a  composition 
for  solo  voice,  violin  or  pianoforte.  Likewise  what  might 
be  a  good  and  acceptable  melody  for  an  inner  part,  alto 
or  tenor,  would  not  be  good  for  soprano  or  bass.  What  is 
necessary  is  that  all  the  voices  should  at  one  time  or 
another  be  melodious,  with  here  and  there  a  chief  melody 
in  one  of  the  parts,  often  accompanied  by  a  melody  of 
secondary  importance  in  another.  There  is  a  wide  field 
between  melodies  of  a  purely  individual,  solo  character 
and  heterogeneous  groups  of  notes  which  are  either  per- 
fectly lifeless  or  at  any  rate  show  no  evidence  of  artistic 
design.  In  music  as  in  everything  else,  life  is  of  the  first 
importance;  and  what  makes  most  for  life  is  motion,  - 
in  its  freest  application,  rhythm. 

§20.  How  true  this  is  may  be  seen  if  we  examine  first 
the  bass  as  the  most  important  of  all  the  parts.  It  is 
obvious  that  starting  from  a  single  note  there  are  only 
three  choices  in  regard  to  motion.  First,  the  note  may 
repeat  itself  once  or  several  times;  or  second,  it  may  move 
stepwise  up  or  down  the  scale  (conjunct  motion);  or  third, 
it  may  move  by  skips,  simple  or  bold  (disjunct  motion).  Of 
these  three  forms  of  activity,  —  repetition,  conjunct  motion 
and  disjunct  motion, — -the  first,  especially  in  the  bass,  is 
the  least  good,  and  the  second,  conjunct  motion,  especially 
from  a  purely  vocal  standpoint,  the  best.  It  is  seldom  of 
good  effect  to  repeat  a  note  in  the  bass,  at  any  rate  in  the 
middle  of  a  phrase  or  period.*  In  so  far  as  this  is  done 
the  bass  part  lacks  life,  variety  and  interest.  If  the  com- 
bination of  chords  is  such  that  the  bass  must  repeat  it- 
self, it  is  often  of  good  effect  to  skip  an  octave  up  and 
down.  In  cadences,  however,  at  the  close  of  a  compo- 
sition, the  dominant  is  often  repeated  intentionally  sev- 
eral times  with  varied  forms  of  dominant  harmony  in 
the  upper  parts,  to  make  the  final  tonic  all  the  stronger 
and  more  satisfying. 


*  In  vocal  music,  however,  the  exigencies  of  the  text  sometimes  cause  repeated 
notes. 


General  Laws  of  Progression 


§21.  Another  blemish  in  a  bass  part,  to  be  avoided  by 
the  student,  is  the  continual  recurrence  of  the  tonic.  This 
renders  the  part  halting  and  weak,  instead  of  free  and 
independent. 


Ex.  (a) 


* 


:5^= 

1 

p 

Example  (a)  is  a  fair  illustration  of  a  type  of  bass  which 
often  occurs  in  students'  exercises.  Its  range  is  far  too 
restricted,  and  the  constant  recurrence  of  the  tonic  makes 
for  monotony  rather  than  for  interesting  variety.  In 
example  (6)  we  have  the  same  bass  part  made  over.  The, 
gain  in  range,  interest  and  in  symmetrical  development 
is  evident. 

Ex.  (b) 


ggi^ 


The  ideal  bass  is  one  which,  starting  with  the  tonic,  ranges 
over  the  various  degrees  of  the  scale  like  a  thing  of  life, 
sometimes  high,  sometimes  low,  and  returns  to  the  tonic 
only  when  it  has  worked  itself  out  to  a  logical  and  gen- 
erally periodic  conclusion. 


(a) 


Examples  of  good  basses 


iS 


SSg: 


a  o  v*  rrr& 


(b) 


26 


Tonal  Counterpoint 


As  the  bass  is  not  only  an  outer  melodic  voice,  but  also 
the  natural  harmonic  foundation  for  the  upper  parts, 
nothing  is  more  important  than  to  acquire  the  power  of 
composing  a  good  bass;  without  this  one  can  never  make 
much  progress  in  any  form  of  composition.  For  this 
purpose  study  and  analyze  carefully  several  basses  of 
Bach,  Beethoven,  Schumann  and  Wagner.  Apropos  of 
the  avoidance  of  the  tonic  in  the  bass  and  considering  the 
part  in  its  harmonic  aspect,  it  is  well  to  bear  in  mind  the 
difference  between  combinations  of  triads  in  the  funda- 
mental position  or  in  the  first  inversion.  Triads  in  the 
fundamental  position  have  a  certain  effect  of  "  inertia, "- 
that  is,  each  one  furnishes  a  more  or  less  satisfactory  stop- 
ping place;  of  the  tonic  triad  in  the  fundamental  position 
this  is  absolutely  true.  It  may,  however,  be  used  on  a  weak 
beat  or  in  such  an  unimportant  relationship  that  its  effect 
is  concealed  or  lessened.  A  piece  of  music  composed 
entirely  of  triads  in  the  fundamental  position  is  much  like 
a  building  formed  of  blocks  of  stone  all  of  the  same  shape. 
The  effect  is  one  of  calm  dignity  and  majesty,  and  is  often 
employed  by  composers  for  a  special  purpose. 


WAGNER.    "  Das  Rheingold 
(a)   Tempo  moderate  c  ira.nqu.illo        •  Walhalla  Motive 


etc. 


(b)  Andante 


CHOPIX.     Op.   ,i7,   No.   i 


General  Laws  of  Progression 


(c)  Allegro  non  troppo 


^W 


TSCHAIKOWSKT.    4th  Symphony; 
Trio  of  jd  movement 


5'j 

^)i  i !?.  k    Ij   |^~    * 

•* !/ 1>  +  r    ^ 


^^ 


ynr 


f 


In  example  (a)  we  see  the  quiet  dignity  inherent  in  com- 
binations of  triads  in  the  fundamental  position;  in  ex- 
ample (6)  a  tranquil  smoothness  gained  in  the  same  way; 
and  in  example  (c)  a  sturdy  strength,  which  is  very  im- 
pressive. But  triads  used  in  this  way  lack  the  plasticity 
and  freedom  which  we  gain  by  placing  them  in  their  first 
inversion.  By  chords  of  the  sixth  our  ears  and  intellect 
are  kept  on  the  "qui  vive,"  and  we  are  impelled  onward 
to  the  final  stopping  place.  It  is  a  safe  general  rule  for 
the  student  learning  to  form  a  good  bass,  to  have  a  fair 
proportion  of  the  notes  in  this  part  imply  first  inversions 
rather  than  to  use  too  many  fundamental  positions.  Great 
attention  should  likewise  be  paid  to  the  fact  that  a  bass 
of  the  best  type  is  not  only  a  good  lower  melody  from  a 
contrapuntal  point  of  view,  but  has  inherent  within  it 
the  implication  of  a  logical  harmonic  fabric  in  the  upper 
voices.  A  beautiful  example  of  a  bass  part  with  this 
double  function  is  cited  from  Beethoven.  Let  the  stu- 
dent harmonize  it  and  then  compare  with  the  original. 

BEETHOVEN.    Op.  14,  No.  2 


Of  the  two  forms  of  real  motion,  conjunct  or  disjunct,  the 
former  is  preferable.     The  best  bass  is  one  which  is  largely 


28  Tonal  Counterpoint 

flowing    (cantabile),    varied   here    and   there   by   effective 

FRANZ.    Four-part  Song 


flowing    ( 
skips,  - — 


generally  simple  ones  such  as  thirds,  fifths,  fourths  and 
sixths,  or  at  times  a  bold  seventh  or  even  ninth,  as  in 
Rheinberger's  song  "  Alpenandacht." 

RHEINBERGER,    Four-part  Song 


Too  many  skips,  however,  make  the  bass  part  disjointed 
and  restless. 

§22.  When  we  come  to  the  soprano  part,  the  greatest 
care  should  be  taken  to  secure,  as  the  normal  type,  a  flow- 
ing and  cantabile  melody  of  sustained  and  varied  interest. 
In  this  voice  a  lifeless  or  monotonous  mass  of  notes  is 
intolerable.  During  the  last  few  centuries  the  soprano 
has  gradually  come  to  be  considered  the  chief  melodic 
voice;  and,  as  it  is  heard  the  most  vividly  and  is  the  most 
easily  followed,  an  intelligently  trained  instinct  will  gen- 
erally produce  a  good  melodious  upper  part.  As  this 
voice  is  exempted  from  the  harmonic  necessities  of  the 
bass,  it  may  be  treated  with  great  freedom.  While  we  are 
learning  to  form  a  good  soprano  part,  a  careful  study  and 
analysis  of  the  works,  even  a  very  few,  of  the  great  com- 
posers will  be  of  more  value  to  us  than  any  number  of 
arbitrary  rules.  Let  us  note  carefully  the  varied  aspects 
of  what  may  be  called  the  "  melodic  curve  "  of  the  great 
melodists;  for  example, 


General  Laws  of  Progression 


SCHUMANN.    Song 


flr";«! 


J J  IJ.JU  J«L 


K 


^3  etc- 


FRANZ.    Song 


To  play  through  and  carefully  analyze  some  of  the  beau- 
tiful songs  of  Schubert,  Schumann  and  especially  Franz, 
will  give  the  student  more  enthusiasm  for  composition 
and  will  be  better  for  the  formation  of  his  melodic  style 
than  to  read  a  dozen  textbooks.  At  first,  until  there  has 
been  acquired  a  well-trained  and  sensitive  judgment  upon 
which  to  rely,  it  will  be  helpful  to  observe  a  few  practical 
suggestions  which  later  on  will  be  recognized  as  somewhat 
mechanical  and  hence  to  be  discarded. 

§23.  Before  we  enter  upon  a  discussion  of  melody  for- 
mation in  its  broadest  sense,  it  is  indispensable  to  acquire 
habits  of  correct  melodic  thought.  As  all  melodies  are 
formed  of  scale  degrees  used  either  in  conjunct  or  disjunct 
motion,  the  first  step  towards  this  end  is  to  realize  just 
which  of  these  degrees  may  be  used  freely  and  which 
imply  a  tendency  towards  certain  subsequent  resolutions. 
Of  course  a  melody  may  progress  diatonically  along  the 
line  of  the  major  or  minor  scale  up  or  down  without  any 
regard  for  tendency  tones.  Some  of  the  smoothest  and 
most  satisfactory  melodies  in  the  realm  of  music  illus- 
trate this  truth;  for  example, 

BEETHOVEN.    Op.  53 


It  is  when  we  wish  to  depart  from  the  simple  diatonic 
movement  and  to  introduce  skips  (disjunct  movement) 


jo  Tonal  Counterpoint 

that  it  is  necessary  to  observe  carefully  which  tones  of 
the  scale  have  an  inherent  tendency  to  progress  along 
certain  lines.  In  connection  with  the  first,  third  and 
fifth  tones'  of  the  scale  (those  which  form  the  tonic  triad) 
there  is  a  certain  inertia.  They  are  under  no  compulsion 
to  move  at  all,  or  in  any  particular  direction.  For  illus- 
tration, in  the  key  of  C  major  let  the  student  strike  any 
one  of  the  notes  c,  e,  g,  successively  in  a  melodic  sense,  or 
together  in  a  harmonic  combination;  in  either  case  there 
will  be  a  feeling  of  repose,  of  inaction.  How  different  is 
the  case,  however,  with  the  remaining  tones  of  the  scale, 
that  is,  the  second,  fourth,  sixth  and  seventh.  After  strik- 
ing any  one  of  these  we  feel  a  distinct  impulse  to  move 
on.  And  that  too,  if  we  follow  the  line  of  least  resistance, 
along  a  definite  path.  As  every  student  well  grounded 
in  harmony  is  aware,  the  tendency  of  these  tones  is  as 
follows:  The  seventh  degree,  or  leading-tone,  progresses 
upwards;  the  fourth  degree  tends  downwards;  the  sixth 
degree  tends  dowmvards,  although  the  tendency  is  not  so 
strong  as  it  is  in  the  case  of  the  fourth  degree.  The  sec- 
ond degree  is  the  freest  of  all,  and  since  by  conjunct  motion 
in  either  direction  it  can  reach  points  of  rest  on  the  tonic 
or  on  the  third  degree,  its  tendency  is  equally  downwards 
or  upwards  (with  a  slight  preference  for  the  former). 
We  find  the  same  tendencies  illustrated  if  we  combine 
the  above  tones  harmonically;  for  example,  the  simplest 
and  most  normal  resohition  of  the  dissonant  chord  b, 
d,  f,  a,  is  as  follows: 


It  is  interesting  to  note  that  a  natural  and  pleasing  melody 
may  be  formed  simply  by  writing  out  these  ordinary  reso- 
lutions in  succession;  for  example, 


In  connection  with  his  studies  the  student  should  analyze 
for  himself  some  standard  compositions.  His  melodic 
instinct  will  be  much  improved  if  he  observes  how  the 
great  composers  in  their  vocal  writings  invariably  follow 
the  tendencies  explained  above,  and  how  even  in  free 


General  Laws  of  Progression 


instrumental    compositions   they    depart   from   them   but 
seldom;  for  example, 


BEETHOVE.V 


4^= 

p=j 

1 

3 

^ 

df.*rrJ.  / 
»       ?  — 

=1=^ 

^ 

6 

s^^ 

4         •>' 

J 

.V   #         .V.  B. 


BEETHOVEN- 


J  . 


In  the  first  measure  of  the  last  example  note  that  the 
progress  diatonically  along  the  normal  scale-line  justifies  the 
irregularity  in  resolution  of  the  fourth  and  of  the  sixth 
degree.* 

§24.  Another  most  important  recommendation  is  that 
in  a  short  soprano  melody  —  for  example,  an  eight- or  a 
sixteen-bar  period  —  there  should  be  but  one  point  of__cli- 
max.  This  may  occur  either  at  the  fifth  or  sixth  measure 
in  an  eight-bar  period;  for  example, 


.  1  tidantc 


FRAXZ.    Op.  ?,  No.  i 


*  For  a  comolete  and  most  interesting  treatment  of  this  whole  subject,  both 
teacher  and  pupil  are  cordially  recommended  to  the  manual  of  Dr.  Percy  Goet- 
schius,  "  Exercises  in  Melody-Writing  "  (G.  Schirmer,  New  York). 


32 


Tonal  Counterpoint 


or  very  often  in  the  third  group  of  four  measures  in  a 
sixteen-bar  period:  for  example, 


Allegro 


BEETHOVEN.    Sonata,  Op.   10,  No.  3 


Climax 


10 


11       12 


13 


14 


15        16 


The  course  of  the  melody  in  this  case  may  lead  up  to  the 
climax  from  the  beginning  and  subside  afterwards  to  the 
end.  Or  the  climax  may  be  saved  for  the  end  itself,  and 
there  may  be  a  gradual  working  up  to  it  from  the  start ; 
for  example, 


Andante  con  moto 


BEETHOVENT.    sth  Symphony 


Climax 


MOZART.     "  Cosi  fan  tutte  " 
0'P'P0m  i  *   ^ 


Climax 


In  general  it  is  not  desirable  that  a  melody  should  start 
in  the  lower  or  middle  part  of  its  range,  should  arrive  at  a 
high  position  either  by  diatonic  motion  or  by  skips,  and 
then,  after  some  aimless  wandering  about,  reach  the  same 
high  point  again.  A  melody,  to  be  sure,  may  often  reach 
in  its  course  a  certain  point  of  interest,  and  then  after  a 
temporary  abatement  of  animation  may  press  on  to  a 
still  higher  point  of  climax.  A  series  of  climaxes  such  as 


General  Laics  of  Progression 


33 


this  is  a  very  common  and  effective  form  of  melody ;  for 
example, 

MENDELSSOHN'.    Scotch  Symphony 


•£J  *  •  m  •,  «•  |        y       |      j        f—i. 


Compare  also   the   following   theme  from  Brahms'  Third 
Symphony : 

Poco  allegretto 


fr+J3j>;.l  I  J^jJ 

• — =_  ^  *  j 


§25.  A  second  useful  recommendation  which  will  make 
for  life  and  variety  is  to  have  the  soprano  voice  move 
through  as  wide  a  range  as  possible;  this  suggestion,  of 
course,  is  to  be  modified  with  reference  to  the  length  of 
the  composition  and  the  simplicity  or  elaborateness  of  its 
style.  That  which  is  strictly  to  be  avoided  is  a  soprano 
part  which  goes  continually  back  and  forth  over  the  same 
few  notes,  or  is  largely  composed  of  meaningless,  frantic 
skips  up  or  down.  In  general,  if  a  special  melodic  effect 
is  to  be  produced,  it  must  not  be  anticipated  in  previous 
measures.  Whatever  its  course,  the  soprano  voice  must 
always  show  design,  and  with  its  mechanical  freedom  of 
motion  : —  be'ing  restricted  only  in  the  lower  part  of  its 
range  by  the  alto  voice  —  tnere  are  very  few  cases  where 
it  cannot  manifest  the  leading  characteristics  of  all  good 
melodic  writing,  — life,  organic  unity  and  variety.  (When 
the  exercises  at  the  end  of  the  chapter  are  worked  out, 
examples  will  be  given  of  bad,  of  ineffective  and  of  good, 
melodious  soprano  parts.) 

§26.  In  dealing  with  the  inner  voices,  the  alto  and  tenor, 
not  so  many  practical  suggestions  can  be  made.  Here 
the  only  way  to  acquire  a  facile  technique  is  to  practise 
steadily  under  competent  supervision.  It  may  be  borne 
in  mind,  however,  that  the  alto  and  tenor  voices  in  gen- 
eral need  not  be  such  free  melodies  as  the  soprano  and 
bass.  In  fact,  thev  could  not  be  if  they  would,  for  they 


34 


Tonal  Counterpoint 


are  hemmed  in  on  both  sides,  the  alto  by  the  soprano 
above  and  the  tenor  below,  and  the  tenor  by  the  alto 
above  and  the  bass  below.  These  two  inner  voices  often 
try  to  avoid  their  restricted  range  by  mutual  adaptation ; 
each  taking  pity,  as  it  were,  on  the  limitations  of  the  other. 
That  is,  the  tenor  crosses  temporarily  above  the  alto  into 
the  highest  part  of  its  range,  while  the  alto  drops  below 
the  tenor  into  its  lowest  register.  Some  of  the  finest 
effects  of  part-writing  for  inner  voices  are  gained  in  this 
way,  as  is  shown  in  the  Madrigals  of  the  early  Italian  and 
English  schools. 


Moderate 


Festa 


,/ 


1 


/ 


f 


S 


inner  voices  cross 


m 


^ 


^ 


Also  further  on  in  the  same  madrigal : 


p  tt  tt 

fo    r  r-r 

nun 

'      1       f       | 
iMWfr  uoicts  or 

OSS 

• 

|{g    tft    (=>         f=^L 

:*    J    J— 
:^rf=f 

P 

TN 

f- 

* 

4>-M  r  r  >i 

r 

:rjF:f 

• 

^      H      1         if 

_pJ  t«J— 

M=i 

In  this  example  let  the  student  note  the  simplicity  of  the 
harmonic  background.  And  yet  beautiful  vocal  effects 
are  produced  by  the  development  of  each  voice  along  in- 
dependent melodic  lines.  We  pre-eminently  see  the  appli- 


General  Laws  of  Progression 


35 


cation  of   this  device  in  the  glorious  living  alto  and  tenor 
voices  of  the  choral  writings  of  Bach : 

BACH.    Choral  from  "  Christmas  Oratorio  " 


Likewise  when  we  come  to  writing  for  strings  we  shall  see 
how  freely  the  parts  for  second  violin  and  viola  cross  and 
interlace.  At  first,  however,  it  will  be  wise  for  the  stu- 
dent to  cross  his  inner  voices  rather  rarely  and  only 
for  a  few  notes  at  a  time.  To  cudgel  his  wits  to  invent 
good  alto  and  tenor  parts  in  their  normal  restricted  group- 
ing will  stimulate  his  imagination  more  than  to  avail 
himself  too  soon  of  the  freedom  of  crossing.  All  music, 
especially  unaccompanied  vocal  music,  must  have  repeated 
notes.  In  fact,  the  repetition  in  the  same  part  of  notes 
common  to  two  or  more  chords  is  the  mechanical  means 
of  homogeneous  chord  connection;  without  this  the  music 
would  entirely  disintegrate. 


(a) 


BA-CH.    Choral 


^^ 


m 


m 


H 


3P 


Tonal  Counterpoint 


BACH.    Choral 


In  example  (a)  note  that  the  alto  is  sustained  while  the 
three  other  voices  move  with  great  freedom;  and  in  ex- 
ample (6)  note  the  fine  effect  of  the  flowing  bass  against 
the  sustained  note  in  the  tenor.  It  is  the  chief  function 
of  the  inner  voices  to  furnish  these  sustained  notes.  They 
are  the  pivots,  so  to  speak,  around  which  swing  the  outer 
voices  with  their  freer  range  and  more  prominent  position. 
So  let  the  student  remember  that  repeated  notes  in  the 
inner  voices  are  not  bad,  but,  on  the  contrary,  desirable. 
He  will  gradually  acquire  facility  in  securing  variety  and 
interest  for  his  inner  voices  where  this  can  be  done  with- 
out too  great  a  sacrifice  in  the  firmness  of  the  harmonic 
texture. 

§27.  A  few  suggestions  will  be  found  helpful  to  the 
student  in  regard  to  melodic  motion  in  general.  As  we 
have  stated  above,  the  motion  should  be  largely  diatonic 
until  there  has  been  acquired  the  critical  judgment  to 
know  just  when  skips  are  effective.  The  skips  which  the 
student  will  naturally  use  first  are  octaves,  fifths,  thirds, 
fourths,  sixths  and  sevenths,  and  about  in  this  order  of 
simplicity.  None  of  these  intervals  will  cause  trouble 
or  need  special  comment  save  the  fourth.  In  the  use  of 
this  interval  the  student  often  goes  astray,  for  in  the  nor- 
mal diatonic  scale  itself  (both  major  and  minor),  from  the 
fourth  degree  to  the  leading  tone,  we  find  the  dissonant 
interval  of  the  augmented  fourth.  From  a  melodic  point 
of  view  we  are  to  remember  that  this  interval  being 
augmented  should  not  be  used  too  often,  and  that  if 
introduced  it  should  generally  keep  on  expanding.  The 
following  are  the  most  natural  and  most  effective  methods 
of  proceeding  from  this  interval : 


General  Laws  of  Progression 

Rare 


37 


fir  f 


that  is,  the  b  goes  up  somewhere;  whereas  the  following 
groups 


are  all  somewhat  unnatural  melodically,  and  their  use 
would  be  justified  only  for  special  effects.  They  occur, 
moreover,  rather  in  instrumental  than  in  vocal  compo- 
sitions.* 


BEETHOVEN. 


Leonore  Overture 


TT 
or 


^Vf^ 


m 


GUI.     Berceuse  for  Violin 
I  f*  m    • 


It  is  well  to  remember  that  this  interval  is  capable  of  freer 
treatment  when  both  notes  are  part  of  the  same  or  re- 
lated harmony,  than  when  the  notes  are  in  two  distinct 
chords.  Practically  in  pure  vocal  writing  these  notes  are 
more  customary  and  more  effective  in  their  inverted  posi- 
tion (a  diminished  fifth).  The  following  melodic  inter- 
vals are  often  very  pleasing: 


The  diminished  fourth,  although  it  will  probably  not  occur 
very  often,  is  a  most  expressive  interval,  and  as  found  in 

*  The  augmented  fourth  is  sometimes  introduced  with  a  downward  progression 
and  produces  a  mysterious,  haunting  effect;  for  example,  in  the  opening  theme  of 
Liszt's  song  to  Goethe's  words,  "  Know'st  thou  the  land  " : 


V 


"Know'st  thou  the  land     where       sweet     the    cit-    ron  blows 


38  Tonal  Counterpoint 

the  minor  mode  from  the  leading  tone  to  the  third  is 
capable  of  very  effective  use.  It  is  rather  more  common 
in  descending  than  in  ascending  passages. 

Both  examples  from  RUBINSTEIN.    Op.  8,  No.  6 


The  minor  seventh,  especially  that  formed  by  the  limits 
of  the  dominant  seventh  chord,  is  a  very  melodious  skip 
and  of  frequent  occurrence  in  the  bass,  especially  ascend- 


ing. 


HANDEL.    "Messiah" 


ITrT 


Likewise  the    diminished    seventh    found    strictly   in    the 
minor  mode,  but  often  used  chromatically  in  the  major:* 


C  minor  or  C  major 


§28.  Before  closing  these  preliminary  suggestions,  a 
few  words  must  be  said  about  the  use  of  the  second  inver- 
sion of  triads,  the  chord  of  the  sixth  and  fourth.  To 
the  young  musician  no  chord  is  more  troublesome  than 
this,  and  yet  when  properly  employed  it  is  one  of  the  most 
useful  and  effective  in  music.  For  the  present  the  student 
is  advised  to  introduce  it  but  seldom,  and  then  with  the 
following  main  principles  of  its  treatment  clearly  in  mind. 
First,  a  six-four  chord  used  on  a  strong  accent  tends  to 
imply  a  cadence  in  that  key  the  tonic  of  which  is  a  per- 
fect fifth  below  or  a  perfect  fourth  above  the  bass  note 

*  The  interval  of  a  minor  seventh  found  in  the  major  mode  between  the  leading 
tone  and  the  sixth  degree  may  also  be  used  with  good  effect;  for  example,  in  the 
well-known  song  of  Tschaikowski : 


J  J 


General  Laws  of  Progression 


39 


of  the  six-four  chord;  for  example,  after  hearing  the  fol- 
lowing six-four  chord  on  g: 


the  listener  is  justified  in   expecting   sooner  or  later  a 
cadence  in  C  major  or  possibly  C  minor;  that  is, 


or 


I  v 


I    V,  V 


This  tendency  is  obviously  strengthened  if  the  positions 
of  certain  voices  in  the  six-four  chord  are  approached  by 
leaps;  for  example,  i 


The  student  will  clearly  understand  the  reason  underlying 


this  cadential  tendency  of 
will  bear  in  mind  that  a  six- 
origin  is  nothing  but  a  triad* 
pension  of  its  third  and  of 
ample,  the  chord 


is  noth- 
ing but' 


six-four  chords  if  he 
four  chord  in  its 
with  a  double  sus- 
its  fifth;  for  ex- 


instead  of 


J 


^g 


We  all  know  that  dominant  harmony,  if  it  moves  along 
the  line  of  least  resistance,  progresses  to  the  tonic  chord. 


*  This  explanation  also  accounts  for  the  well-known  rule  in  regard  to  doubling 
—  "  in  six-four  chords,  double  the  bass,"  that  is,  the  note  which  is  really  the  root. 


Tonal  Counterpoint 


It  by  no  means  follows  that  this  simple  resolution  must  be 
the  one  chosen  in  every  given  case, 
for  by  the  principle  of  "  Deceptive 
Cadences,"  already  familiar  to  the 
student  (see  above,  p.  22),  the  chord 


or 


may  progress  in  countless  directions.      Just  so  a  six-four 
chord  when  used  on  a   strong"  accent,  need  by  no  means  f 
result   invariably  in  a   cadence  in  the  given  key.     After 
a  six-four  chord,  a  deceptive   cadence   is    often    used;  for 
example, 


J. 


C:  I 


CV  I 


But  nevertheless  the  fundamental  principle  remains  that 
an  accented  six-four  chord  arouses  an  expectation  of  a 
cadence  in  the  key  the  tonic  of  which  is  a  fifth  below  or  a 
fourth  above,  and  this  natural  expectation  if  not  satis- 
fied must  be  compensated  by  smooth  and  interesting 
modulatory  resolutions  into  other  keys  (as  shown  above). 
The  inference  from  all  this  is  plain :  accented  six-four 
chords,  in  particular  those  derived  from  the  tonic  of  the 
given  key,  should  seldom,  if  ever,  be  introduced  in  the 
middle  of  a  musical  sentence  or  phrase  (that  is,  we  do  not 
wish  to  stop  in  the  middle  of  anything).  Second,  six-four 
chords,  those  derived  from  the  tonic  triad  or  from  any 
triad  in  the  key,  are  often  used  on  weak  beats,  that  is,  in 
an  unaccented  relationship  to  the  chords  preceding  and_ 
following.  In  this  case  the  six-four  chord  is  a  passing 
chord;  several  or,  all  of  the  voices  should  move  diatonic- 
ally,  and  the  fonft%t>m  the  six-four  chord  is  almost  invari- 
ably held  over  in  the  same  voice  from  the  preceding  chord. 
The  following  phrases  illustrate  this  very  common  usage: 

(a) 


fihp 

|  *| 

i 

j  j  j 

i  J  1  i  i 

«r 

1=H 
H 

PE 

2 

8« 
-*>•• 

r 

i  r       i 

'  r  r  r  1 

P  f    r 

General  Lai^s  of  Progression 


ir%  J  c 


m 


- 
J  J 


J  J 


P     n    —a     a    — ~     g    -p 

r  r  i  f  r  i  [•  f  i 


vi  IV 

In  each  of  the  above  examples  the  second  inversions  are 
used  as  passing  chords, —  that  is,  they  are  on  weak  beats, 
and  the  parts  move  diatonically,  or  when  this  is  not  the 
case,  one  part  at  least  is  held  over  from  the  preceding 
chord  as  in  the  second  measure  of  example  (6).  Therefore 
in  connection  with  no  one  of  them  do  we  feel  a  cadential 
tendency  towards  any  particular  tonic,  and  their  use  in 
the  middle  of  a  phrase  is  justified.  Third,  chords  of  the 
sixth  and  fourth  may  be  freely  used  between  other  posi- 
tions of  the  same  chord;  for  example, 


or  when  they  are  preceded  and  followed  by  a  triad  in  the 
fundamental  position  on  the  same  bass  note: 

V 

WESLEY.    Hymn  Tune 


* 

i  J      ||| 

III    ill 

I     i      II 

W=    -f- 

,    J 

J  jl  J 

Eg  —  -J  —  9  — 

m 

—  a*  — 

r 

r  r  r  r  i 

i       i 

t-rr 

rrrr 

r 

§29.  The  student  is  cautioned  against  the  use  of  suc- 
cessive second  inversions,  especially  when  the  bass  moves 
by  skips.  The  following  combinations  are  very  bad : 


Tonal  Counterpoint 

bad 


Successive   six-four   chords   are,   to   be   sure,   occasionally 
seen;  for  example. 


It  is  evident,  however,  in  the  above  example  that  the  second 
six-four  chord  has  no  real  harmonic  import,  but  that  the 
effect  is 


The  two  grace  notes  before  the  tonic  chord  are  then  length- 
ened, and  the  first  six-four  is  merely  a  passing  chord  be- 
tween two  positions  of  tonic  harmony.*  It  is  not  to  be 
inferred  that  the  above  statements  include  all  the  pos- 
sible uses  of  the  six-four  chord,  they  simply  indicate  the 
general  method  of  treatment.  In  actual  music,  examples 
may  be  found  of  second  inversions  derived  /from  every 
triad  of  the  scale,^  though  the  super-tonic  and  mediant 

*  For  a  beautiful  example  of  successive  chords  of  the  sixth  and  fourth  with  a 
diatonic  bass,  let  the  student  consult  the  seventh  and  eighth  measures  of  the  first 
movement  of  Mozart's  C  Maior  Symphony. 

t  For  a  classified  list  of  such  chords  of  the  sixth  and  fourth  the  student  is 
advised  to  consult  the  sixth  chapter  of  Prout's  Harmony. 


General  Laws  of  Progression 


43 


triads  are  comparatively  rare  in  this  position.  As  a  last 
word  we  may  say  that,  in  general,  second  inversions  may 
be  introduced  without  bad  effect  whenever  the  voices, 
and  in  particular  the  bass,  move  diatonically  ;  for  example, 


vm 


f 


s& 


^ 


Here  Mendelssohn  in  his  march  from  "  Athalie  "  intro- 
duces on  a  weak  part  of  the  measure  a  second  inversion  of 
the  mediant  triad  (note  that  the  bass  moves  diatonically). 
Six-four  chords,  however,  when  introduced  by  a  leaf,  are 
to  be  used  with  great  caution.  The  following  combina- 
tions, for  example,  would  be  very  bad: 


[^ 

-^1 

T-ih 

Tp  —  I  —  e  — 

-^—- 

^t 

As  to  the  best  effect  of  a  six-four  chord  in  any  given  case 
nothing  but  patient  practice  will  give  the  student  the 
mature  judgment  and  the  unerring  artistic  sense  for  such 
decision. 

§30.  It  is  taken  for  granted  that  every  one  is  familiar 
with  the  normal  range  of  the  voices.  In  general  the 
soprano  should  not  be  taken  above  and  the  bass 


No  one  of  the  voices  should  be  kept  for  long  either  in  the 
highest  or  the  lowest  part  of  its  range.  For  voices  the 
writing  must  be  comfortable  and  grateful  to  the  singers. 
All  the  following  exercises  should  be  worked  out  in  open 
score,  —  that  is,  with  each  voice  on  a  staff  by  itself;  and  as 


44  Tonal  Counterpoint 

soon  as  possible  the  appropriate  clefs  should  be  used  in 
connection   with  the  inner  voices, — that  is,    for  the  alto 


voice 


and  for  the  tenor 


From  the  very  outset  the  student  should  endeavor  to 
think  of  the  tenor  part  in  connection  with  this  clef,  as 
the  notation  of  a  tenor  voice  is  most  unsatisfactory  when 
written  in  either  the  F  or  in  the  G  clef.  A  tenor  part  in 
the  F,  or  violin  clef,  is  sung  an  octave  lower  than  the 
written  notes  would  imply;  for  example, 


Sune  an  octave  lower 


On  the  other  hand,  if  the  G  or  bass  clef  is  employed,  a  con- 
stant use  of  leger  lines  is  necessary  to  keep  the  tenor  in 
the  best  part  of  its  range.  More  than  half  the  time 
the  notes  will  be  off  the  staff;  for  example, 


The  first  exercises  therefore  should  be  written  with  the 
following  combination  of  clefs : 


Supram 


Altc 


Ten. 


Bass 


Gradually,  as  the  student  acquires  facility,  the  appropri- 
ate alto  clef  may  be  introduced.     The  first  melodies  given 


General  Laws  of  Progression  45 

are  placed  in  the  bass,  and  the  upper  voices  are  to  be 
added,  particular  care  being  given  to  the  formation  of  a 
good  soprano.  Others  are  placed  in  the  soprano,  and  in 
this  case  still  more  attention  must  be  given  to  the  bass 
part  which  must  be  a  good  harmonic  foundation  and  also 
a  flowing,  singable  melody.  It  is  advisable  that  certain 
of  the  melodies  be  placed  in  an  inner  voice.  Too  much 
time,  however,  should  not  be  given  to  this,  until  consider- 
able facility  has  been  acquired.  No  special  directions  are 
given  as  to  what  harmonic  scheme  should  be  used  in  any 
given  case.  From  his  study  of  harmony  the  student  is 
supposed  to  have  stored  up  a  certain  fund  of  simple  and 
effective  harmonic  combinations.  These  he  is  now  to 
apply  under  the  guidance  and  criticism  of  the  teacher. 
In  acquiring  a  technique  in  composition  his  aim  should 
be  to  proceed  from  "  the  simple  to  the  complex."  At 
first,  therefore,  in  these  short  and  simple  exercises  it  is 
better  to  use  triads  almost  exclusively.  Now  and  then 
dominant  seventh  harmony  may  be  introduced,  and  grad- 
ually secondary  sevenths.  In  general,  augmented  chords, 
altered  chords  and  other  complicated  harmonies  should 
be  reserved  for  longer  and  more  elaborate  melodies.  As 
to  modulation  the  student  should  try  to  express  as  much 
as  possible  by  using  the  resources  of  one  key.  If  a  modu- 
lation is  made  whenever  a  difficulty  is  encountered,  much 
valuable  practice  is  lost.  Interest  and  variety  should 
be  sought  by  changing  the  positions  and  progressions  of 
the  chords  in  a  given  key.  Now  and  then  modulations 
may  be  made  to  nearly  related  keys,  and  at  times  some 
particular  modulation  is  clearly  implied  by  the  melody 
itself.  Three  melodies  in  the  bass  are  now  harmonized 
to  show  the  general  style  to  be  adopted  in  subsequent 
work : 

(a) 


/•   rH-    ft     ?5     " 

i"7~ 

~P  

rr~ 

— 

- 

n  — 

—  19  1 

J.  — 

-&— 

rj  — 

'   1] 

-|  

- 

=j  

-|  

-M 

As  this  is  a  diatonic  melody  of  the  simplest  type,  a  har- 
monic structure  composed  of  triads  in  different  positions 
would'  certainly  be  appropriate.  Following  the  recom- 
mendations for  simple  triad  connection  cited  above,  we 
produce  this  harmonization,  in  which  our  aim  has  been 
first  to  write  clear  harmony;  second  to  form  a  good 


46 


Tonal  Counterpoint 


soprano;  and  third  to  make  the  inner  voices  as  varied  as 
possible. 

(a) 


tf      .J 


s      6 


6    6 


As  to  the  harmony,  note  the  preponderance  of  chords  of 
the  sixth.  Follow  the  melodic  line  of  the  soprano,  which 
starts  (rather  exceptionally)  in  a  high  position,  works 
smoothly  down  the  scale  and  then  rises  by  simple  leaps 
to  a  point  of  climax  at  the  end.  The  inner  voices  are  not 
so  flowing  or  so  varied  in  melodic  outline  as  the  bass  and 
soprano.  Still  repeated  notes  have  generally  been  avoided, 
the  alto  is  singable,  and  the  tenor  has  at  least  the  variety 
of  a  fairly  wide  range.  We  now  give  a  bass  melody  which 
will  allow  a  more  varied  harmonization: 
(ft) 


As  this  melody  is  in  the  minor  mode,  before  we  begin  to 
harmonize  we  think  what  are  the  most  effective  harmonic 
combinations  in  that  mode,  and  we  also  bear  in  mind  the 
necessity  of  raising  the  seventh  degree  ( f #  ) : 

rcjL 


General  Laws  of  Progression 


47 


This  exercise,  simple  though  it  be,  will  repay  careful  analy- 
sis. First,  as  to  the  harmonic  structure,  at  (a)  dominant 
seventh  harmony  has  been  used,  and  at  (b)  an  inversion 
of  the  diminished  seventh  chord.  From  the  third  to  the 
fifth  measure,  the  inner  voices  are  made  more  varied  in 
range  by  a  change  in  position  of  the  chords.  As  far  as 
harmony  alone  is  concerned,  the  exercise  at  this  point 
might  have  been  written  thus: 


s 


0,  \> 


Here  the  alto  and  the  tenor  are  unnecessarily  lifeless, 
even  for  inner  voices.  In  cases  like  this  a  change  of  posi- 
tion will  often  secure  at  least  variety  of  range.  In  regard 
to  the  soprano,  as  at  first  it  goes  smoothly  up  and  down 
the  scale,  towards  the  end  it  is  enlivened  by  two  ascend- 
ing skips  of  a  fourth,  and  finally  at  (c)  by  the  introduction 
of  that  interval,  so  characteristic  of  the  minor  mode,  the 
diminished  seventh.  At  (d)  a  passing  note  is  used,  to 
give  the  alto  a  flowing  final  phrase.  The  student  has 
doubtless  learned  the  main  rules  in  regard  to  passing  notes 
from  his  studies  in  harmony,  and  although  a  complete 
account  of  their  treatment  is  reserved  for  a  subsequent 
chapter,  even  in  these  simple  exercises  they  may  occa- 
sionally be  introduced,  especially  in  the  inner  voices,  when- 
ever those  parts  would  otherwise  be  monotonous  or  lack 
a  melodious  flow. 

(c) 


We  now  attempt  an  exercise  which  will  allow  passing 
modulations  into  related  keys.     More  passing  notes  also 


4<V  Tonal  Counterpoint 

will  be  introduced  to  show  their  great  use  in  the  develop- 
ment of  a  flowing  style : 


m 


m 


?'Vi  ij  J 


6  6 


A:>        E?        C 

In  this  version  the  harmonic  structure  is  simple;  yet  con- 
siderable variety  is  obtained  by  modulating  into  the  major 
keys  of  Ab  and  E!>.  Play  over  each  of  the  voices  by  it- 
self, and  note  that  by  the  use  of  passing  notes  each  of 
the  inner-  parts  becomes  an  entirely  satisfactory  melody. 
The  soprano  is  noticeable  for  its  wide  range;  a  minor-tenth 
in  eight  measures.  At  (a)  the  augmented  fifth  of  dominant 
seventh  harmony  ha,s  been  introduced,  and  at  (6)  the 
rhythm  is  varied  by  a  suspended  note.  At  (c)  in  the 
tenor,  note  the  melodic  form  of  the  minor  scale. 

$31.  Melodies  in  the  bass  to  be  treated  as  indicated; 
those  which  are  short  like  examples  (a).  and  (6);  the  longer 
ones  like  (c). 


Like  (a) 


1. 


Like  (a) 


General  Laws  of  Progression 

Like  (a) 

*-  yd-i  j  j  iJHi'p 


49 


Like  (a) 


Like  (o) 


6.    *. 


Like  (6) 


Like  (b) 


j  i t~l — r 

g       f"1     fi»    h^       M 

r '  i  r '  ^ '  ** 


Like  (6) 


Like  (c) 


J    I     I     J     [ 
^ 


x, 
1 


Like  (e) 

i.P*£ 


[   i    i     I    i    -I 

<J    J  » •  M 


§32.  We  now  harmonize  three  typical  melodies  in  the 
soprano  as  models  for  analysis: 


•|< 


ri    i.i  ji.  •i(<rifir 


jo  Tonal  Counterpoint 

This  melody  will  be  recognized  as  the  same  one  treated 
above  in  §30  in  the  bass: 

(a) 


cyyi 

«] 

4= 

^ 

— 

- 

pd 

S>     2  TJ 

- 

m 

tt 

E 

J 

J-  J 

w 

* 

6 

o.-t^ar  r 

2 

M 

- 

6 

^ 

I 

/   «  a  '  

f 

—  1- 

LnJ 

This  version  calls  for  no  especial  comment ;  the  simplicity 
of  the  melody  would  not  allow  elaborate  inner  parts.  At 
(a)  note  the  descent  of  the  leading  tone  in  an  inner  part 
to  gain  a  complete  final  chord: 


^  ^,>  4     1  1   J 

^=F= 

grh4j=*d|,«|«Mg       --l-^ai 

I|J    1    ')*    11 

^ 


^ 


^ 


i>">   3 


H?I.> 

"    !i       •* 


i 


P 


In  this  version,  simple  though  the  harmonic  structure  be, 
acceptable  alto  and  tenor  voices  have  been  secured.  The 
bass  is  thoroughly  good;  it  is  vital  in  motion,  and  broad 
in  range.  Note  at  (a)  the  effective  descent  of  a  minor 
seventh : 


(O 


r  r 


General  Laws  of  Progression  51 

This  melody  may  be  treated  in  a  somewhat  freer  style; 
secondary  seventh  chords  may  be  introduced,  and  passing 
modulations  made  to  related  kevs. 


*P 


o    a 


P 


m 


P 


In  this  version  repeated  notes  are  freely  used,  especially 
in  the  inner  voices.  Still  the  general  course  of  both  the 
alto  and  of  the  tenor  is  varied  and  melodious.  In  the  last 
two  measures  of  the  bass,  note  the  vigor  of  the  successive 
leaps  of  a  perfect  fifth. 

§33.  Melodies  in  the  soprano  to  be  treated  like  the  above 
models. 

Like  (a) 


m 


Like  (a) 


2. 


Like  (c) 


3. 


-q-72 


Like 


Tonal  Counterpoint 


Like  (c) 


5. 


*4= 

£p 

TTR 

-*- 

itf  1  1 

JJJJ 

Like  (c) 


.vi  '  *<  Its! 

q3L 

P-I 

=±1= 

-H 

— 

- 

1    1  1 

'rn  " 

Like  (c) 


Jfci 

3 

Mil 

'  r 

:rF=F 

A/'.  5.  —  In  this  melody  a  good  effect  may  be  produced 
by  beginning  in  D  minor  and  ending  in  the  relative  major. 


Like  (c) 


I 


9-     (fe  a  J  I  J  J  I  j  j  I J  J  I  f  H  P  H  J  J  I  f  J 


J      f 

g>    | 


No.  9  is  to  be  harmonized  mostly  with   combinations  of 
triads,  in  keeping  with  the  simplicity  of  the  melody. 


General  Laws  of  Progression 


53 


This  melody,  although  longer  than  those  first  given,  can 
be  harmonized  in  the  same  simple  style.  One  modulation 
is  indicated  into  the  related  key  of  B  minor.  Early  in 
this  course  of  study  the  "371  Four-voiced  Chorals  "  of 
J.  S.  Bach  should  be  procured,  and  the  student  to  whom 
work  on  the  above  melodies  has  been  fairly  easy  may  now 
harmonize  some  chorals  or  at  any  rate  phrases  from  them. 
It  is  left  to  the  teacher  to  direct  this  part  of  the  work  in 
accordance  with  the  advancement  and  facility  of  each 
particular  student.  Numbers  258,  38,  26,  293  and  6  are 
recommended  as  suitable  for  treatment  at  this  stage  of 
the  work.  Many  interesting  and  stimulating  examples 
may  be  looked  up  from  the  works  of  the  great  composers 
to  show  what  fine  effects  can  be  produced  in  four-part 
writing  with  very  simple  means.  Two  such  illustrations 
are  herewith  cited: 


Tempo  giusto 


HANDEL.    "  Judas  Maccabaus,"  No.  52 


P=H 

- 

1 

=H 

- 

?  —  f 

7 

--f 

7 

4 

n 

— 

F 

3 

- 

^- 

7 

3 

fe 

| 

r- 

= 

f 

L. 

=i 

Although  this  passage  is  entirely  wanting  in  rhythmical 
contrast,  observe  how  freely  the  voices  move. 


MENDELSSOHN.     "Athalie,"  No.  z 


c\ 


fTw- 

^ 

s 

1 

J 

— 

/• 

F 

^=f 

^ 

=f 

N 

tf 

? 

f 

t. 
^ 

^ 

')'•  S  S 

^ 

a 

N 

s 

54 


Tonal  Counterpoint 


(a) 


rts 


tfr* 

^ 

'•  -pH 

=F 

=£*= 

F^= 

fa 

—\  — 

—  0- 

- 

^ 

* 

3= 

*t 

. 

f^ 

| 

— 

=£p 

=P=P= 

=£ 

1= 

L 

iL-k  — 

J  [—I 

—  1  —  1—  ^  —  U 

Play  through  each  voice  by  itself;  observe  the  melodious 
tenor  part  in  the  third  phrase,  and  the  striking  effect  of 
the  secondary  seventh  chord  at  (a).  To  analyze  care- 
fully the  part-writing  found  in  the  magnificent  opening 
choral  of  Wagner's  "  Mastersingers  "  will  also  be  benefi- 
cial and  inspiring  to  the  student. 

§34.  Short  melodic  phrases  should  now  be  placed  both 
in  the  alto  and  in  the  tenor,  and  four-part  harmoniza- 
tions worked  out.  Even  though  the  harmonic  structure 
be  very  simple,  our  work  now  becomes  considerably  more 
difficult,  for  whenever  the  chief  melody  is  in  either  of  the 
inner  voices,  we  must  form  in  the  same  exercise  both 
a  good  harmonic  bass,  and  a  free  melodious  soprano. 
Facility  and  sureness  in  this  style  of  writing  are  acquired 
only  little  by  little  and  by  constant  methodical  practice. 
The  student  therefore  should  not  be  discouraged  if  at 
first  the  work  seems  difficult.  From  the  very  outset, 
however,  in  contrapuntal  study,  we  must  recognize  the 
fact  that  the  chief  melody  is  often  in  one  of  the  inner 
voices.  A  merely  cursory  examination  of  the  standard 
compositions  for  the  pianoforte,  for  string  quartet,  and 
especially  for  orchestra,  will  convince  the  student  how 
free  music  is  in  this  respect.  Sometimes  the  principal 
melody  is  in  the  soprano,  sometimes  in  the  bass,  often 
either  in  the  alto  or  in  the  tenor.*  In  the  following  exer- 
cises although  the  soprano  is  a  secondary  melody,  it  must 
still  have  motion,  and  as  much  variety  in  range  as  the 
circumstances  will  allow.  Hence  repeated  notes  should 
seldom  be  employed.  For /instance,  if  we  were  asked  to 
harmonize  this  melody  in  the  alto, 

*  The  teacher  can  easily  refer  the  student  to  characteristic  examples  from  the 
compositions  of  Beethoven,  Schumann,  Wagner,  Brahms  and  others. 


General  Laws  of  Progression 


55 


. I  .11. 1  .11.1  Jlj 


the  following  version  would  be  very  bad  on  account  of  the 
monotony  of  the  soprano.  The  skips  in  the  latter  part 
of  the  bass  are  also  rather  aimless : 


A   satisfactory    version   should   be   in   style    somewhat 
like  the  following: 


i 


m 


m 


m 


In  the  above  version  we  have  gained  melodic  freedom  for 
the  soprano,  and  the  skips  at  (a)  afford  a  good  contrast 
to  the  sustained  notes  in  the  alto.  The  bass  part  also  is 
more  symmetrical  than  in  the  first  version.  Almost  any 
of  the  melodies  in  the  preceding  paragraphs  are  available, 
when  properly  transposed,  for  use  in  the  alto.  For  ex- 
ample, in  §31,  No.  i  may  be  transposed  into  C  major  and 
placed  in  the  alto.  Xo.  2  may  be  transposed  into  D  major. 


^6  Tonal  Counterpoint 

In   §32,  example   (a)   may  be  transposed  into   Eb    major. 
We  add  a  few  longer  subjects  for  treatment  in  the  alto: 


1. 


J    I    J    J  I  J   Jl  J    J   I   j  J 


l.l  JI.I..I  U 


3. 


A/".  J5.  —  In  this  exercise  secondary  seventh  chords 
may  be  introduced  with  good  effect,  especially  in  measures 
four  to  six. 

§35.  We  now  work  a  harmonization  with  the  following 
melody  in  the  tenor: 


0    i 

r  i 


and  then  give  several  tenor  melodies  to  be  treated  like 
those  above  in  the  alto. 


tim 

P 

y 

1 

= 

= 

= 

— 

= 

^ 

: 

o 

H 

=1= 

• 

! 

f= 

4 

General  Laws  of  Progression 
Subjects  in  tenor: 


57 


'*H['  f  i  r  f- 


*- 


£hM 


irnrrrirnrrip 


CHAPTER  II 
Two-Part  Counterpoint  —  First  Order 

[Although,  for  the  sake  of  simplicity,  we  begin  our  con- 
trapuntal studies  with  counterpoint  of  the  first  order,  that 
is,  the  notes  of  each  part  are  to  be  of  equal  value,  it  is  not 
advisable  to  remain  long  on  these  exercises,'  which  in  their 
very  nature  are  somewhat  monotonous  and  uninteresting. 
As  we  are  using  only  two  parts,  the  harmony  must  neces- 
sarily be  thin,  and  the  chords  may  often  be  ambiguous; 
and,  the  notes  of  the  two  parts  being  of  equal  value,  we  are 
restricted  from  all  variety  of  rhythm,  which  in  actual 
music  is  one  of  the  chief  means  of  contrapuntal  effect. 
Furthermore,  no  matter  what  range  we  arbitrarily  select, 
the  two  parts  are  heard  as  outer  voices;  and,  as  the  harmony 
implied  by  them  must  in  most  cases  be  just  as  natural  and 
clear  as  if  all  the  parts  were  actually  written  out,  there 
seems  to  be  no  valid  reason,  as  long  as  we  are  writing 
"  note  against  note  "  why  we  should  not  rather  practise 
in  jour  real  parts.  In  actual  compositions  for  voices, 
strings  or  for  pianoforte,  there  would  never  be  a  case, 
except  for  a  few  measures  at  a  time,  when  we  should  write 
in  two  parts  without  having  them  move  in  notes  of  differ- 
ent values  and  in  varied  rhythm.  Almost  no  case  can  be 
found  in  standard  compositions  of  a  two-part  sentence  in 
notes  of  equal  value.*  The  following  example,  a  Swiss 
Song  which  Beethoven  uses  as  a  theme  for  six  variations, 
is  noteworthy: 

Andante  con  moto 


*  In  the  opening  measures  of  the  Scherzo  of  Beethoven's  Trio,  Op.  97,  written 
in  two-part  harmony,  the  student  may  sec  for  himself  how  important,  even  in 
the  simplest  style,  is  variety  of  rhythm. 

58 


Two-Part  Counterpoint  5P 

On  the  other  hand,  just  because  the  voices  are  few  and  the 
harmonic  effects  limited,  these  simple  two-part  exercises, 
if  studied  in  the  right  way  (as  means  to  an  end)  afford 
valuable  rudimentary  practice  in  the  facile  handling  of 
the  common  intervals  and  in  melody  formation.  They 
may  be  considered  as  exercises  in  pure  design,  and  the 
student  should  gain  from  them  a  quickened  ingenuity  and 
the  ability  to  look  at  voices  horizontally,  that  is  through- 
out their  range,  as  interesting  flowing  melodies.  The 
subjects  given  at  the  end  of  the  chapter  have  been  made 
as  melodious  and  varied  as  possible,  and  modulations  into 
neighboring  keys  are  implied.  No  matter  how  carefully 
the  exercises  are  worked  out,  the  question  should  hardly 
be  raised  as  to  whether  they  are  beautiful  or  not.  This 
mistake  is  often  made  by  beginners  in  counterpoint.  The 
problem  is  akin  to  that  of  the  man  who  is  given  six  straight 
sticks  and  told  to  arrange  them  in  an  ingenious  and  inter- 
esting way.  Two-part  writing  from  an  artistic  point  of 
view  is  one  of  the  most  difficult  forms  of  composition,  and 
presupposes  not  only  a  complete  knowledge  of  every  con- 
trapuntal device,  but  a  special  study  of  the  proper  style 
of  writing  for  strings  or  for  pianoforte.*  After  the  stu- 
dent has  acquired  facility  in  the  different  varieties  of  con- 
trapuntal effect,  he  may  try  some  two-part  writing  which 
it  is  to  be  hoped  will  sound  beautiful  or  at  any  rate  be  full 
of  life  and  individuality.  These  exercises  are  merely  the 
first  necessary  steps  to  that  end,  and,  to  use  terms  from  a 
kindred  art,  they  may  be  said  to  teach  the  student  to 
draw,  that  is,  to  appreciate  the  constructive  necessity  of 
lines  and  curves  in  order  that  later  he  may  paint  with 
intelligently  grouped  colors.] 

§36.  In  two-part  counterpoint  note  against  note,  since 
the  effect  is  of  necessity  somewhat  thin  and  vague,  we 
select  for  intervals  between  the  two  voices  those  which 
give  the  feeling  of  complete  and  definite  harmony;  that  is, 
major  and  minor  thirds  and  sixths  and  the  perfect  con- 
cords, the  unison,  the  octave  and  the  perfect  fifth  (not  the 
perfect  fourth,  since  it  indicates  a  second  inversion!).  Of 
these  intervals  the  unison  is  seldom  available  except  on 
the  first  or  on  the  last  note;  in  the  body  of  an  exercise 

*  It  is  noteworthy  that  Bach,  that  great  master  of  counterpoint,  writes  only  one 
Fugue  in  two  parts;  the  one  in  E  minor,  No.  10  in  Book  I  of  the  "  Well-tempered 
Clavichord."  Many  of  the  Preludes,  however,  are  largely  in  two-part  style. 

t  The  student  is  often  troubled  by  the  discrimination  between  perfect  fifths  and 
perfect  fourths,  although  each  interval  when  taken  by  itself  has  an  empty,  thin 
sound.  '_The  reason  is  this:  when  a  perfect  fifth  is  introduced  in  a  proper  harmonic 
context  it  outlines  a  major  or  minor  triad,  and  the  imagination  of  thr>  hearer  sup- 


6o 


Tonal  Counterpoint 


thirds    and    sixths    should    predominate,    because    they 
define   the   harmony  better;   for   example, 

ft  (a)    Cb)    (c)    (d) 


From  example  (a)  we  do  not  know  whether  a  major  or  a 
minor  triad  is  implied;  the  minor  sixth,  however,  at  (b) 
must  represent  the  first  inversion  of  the  triad  g,  b,  d.  Of 
course  example  (b)  could,  as  far  as  mere  notes  go,  stand  for 

the  second  in-     » version  of  the  triad  e,g,b, but, when 

the    interval  ~tL  |   is   played,    the    ear    instinctively 

supplies  a  d  ffi  (S)  "  and  not  an  e.  That  is,  every 
two-part  6  combination  tends  to  represent 
either  a  fundamental  position  or  a  first  inversion,  but 
not  often  a  chord  of  the  sixth  and  fourth  (consult 
§28  in  Chapter  I).  A  moment's  thought  will  show  us 
that  there  is  a  certain  ambiguity  in  the  case  of  thirds  and 
octaves;  for  example,  example  (c)  above  may  stand 
either  for  the  fundamental  position  of  the  triad  d,  f,  a, 
or  for  the  first  inversion  of  the  triad  b,  d,  f.  In  like 
manner  the  octave  at  (d)  may  represent  a  doubled  root 


of  the  triad  e,  g,  b;  that  is, 


plies  the  missing  third;  for  example,  the  following  perfect  fifth 


invariably  suggests  either         fiK    ij     llor'ffT~^~1l      and  sonletimes  so  adequately 

*T  «.  .«»- 

as  hardly  to  sound  empty  at  all.     Whereas  a  perfect  fourth 


not  being  the  outline  of  any  fundamental  harmony  (except  an  incomplete  second 
inversion)  remains  a  mere  thin  and  unsatisfactory  interval,  unless  it  is  immediately 

followed  by  a  third 


in  which  case  the  f  is  practically  a  suspended  note;  for  example      fiK 

and  the  interval  of  the  fourth  is  felt  to  have  no  harmonic  impi  >rt  ~P" 

whatsoever. 


Two-Part  Counterpoint 


61 


or  a  doubled  third  of  the  triad  c,  e,  g;  that  is,    3t 


At  first  the  student  should  accustom  himself  to  think  very 
clearly  just  what  chords  are  outlined  by  the  two  voices. 

§37.  The  parts  should  in  general  proceed  diatonically, 
although  skips  of  major  and  minor  thirds,  perfect  fifths  and 
fourths,  major  and  minor  sixths  and  octaves  may  be  freely 
used  for  the  sake  of  melodic  variety.  Skips  of  a  seventh 
and  of  all  augmented  and  diminished  intervals  should  be 
avoided  for  the  present.  The  diminished  fifth,  however, 
may  occasionally  be  introduced  with  good  effect,  if  care 
is  taken  to  resolve  the  second  note  to  a  note  within  the 
original  interval;  for  example, 


1.5'.* 


£ 


^ 


s 


§38.  Contrary  motion  between  the  two  voices  is  gener- 
ally desirable,  whenever  the  harmonic  scheme  will  allow 
it,  although  parallel  motion  is  often  quite  necessary  for 
a  while.  The  monotony,  however,  of  more  than  three 
successive  thirds  or  sixths  is  to  be  strictly  avoided;  for 
example, 


T 


fr 


or 


,0      _    '    (J      1-3    i  \*     rJ 

r  r  f  r  r  r 


In  such  combinations  as  these,  each  melody  is  merely  a 
weak  imitation  of  the  other  in  a  different  part  of  the  scale, 
and  all  independence  and  contrast  of  melodic  design  (the 
very  essence  of  contrapuntal  writing)  is  lost. 

§39.  Perfect  parallel  fifths  and  octaves  are  of  course 
strictly  forbidden,  and  even  in  regard  to  concealed  fifths 
and  octaves,  in  two-part  counterpoint  the  rule  forbid- 
ding them  should  generally  be  followed.  The  student  is 


62 


Tonal  Counterpoint 


reminded  that  concealed  fifths  and  octaves  are  questionable 
when  both  voices  are  outer  ones,*  when  they  both  skip, 
when  they  both  ascend,  when  one  voice  moves  a  whole 
tone;  for  example,  the  following  combinations  are  all  bad 
in  two-part  writing: 


On  the  other  hand,  when  the  consecutives  are  between 
an  inner  and  an  outer  voice,  or  better  still  between  the 
two  inner  voices,  when  the  voices  descend  and  when  one 
part  moves  step  wise  (especially  by  a  semitone),  consid- 
erable freedom  is  available  even  in  two-part  writing. 
Even  with  ascending  voices  a  concealed  octave  is  of  good 
effect  if  the  upper  part  is  approached  by  a  semitone.  The 
following  combinations  are  all  good,  and  may  be  freely 
used: 


n 


JjuLJ, 


possible        better 


M 


J 


n    9.     fJ    II 

P^P 


^1 


p 

r 


§40.  Two  successive  major  thirds  are  to  be  avoided,  — 
unless  the  step  between  them  be  that  of  a  minor  second, 
as  in  the  progression  V-VI  or  VI-V  in  the  minor  mode;  for 
example,  , 


VI  VI   V 


for  they  outline  the  objectionable  interval  of  an  augmented 
fourth;f  f°r  example, 


*  Certain  of  these  general  considerations  are  applicable  only  to  counterpoint  in 
more  than  two  parts;  it  has  already  been  stated  that  in  all  two-part  writing  the 
voices  must  be  harmonically  outer  voices. 

t  In  actual  composition  this  is  to  be  taken  more  as  a  recommendation  than  as  a 
hard  and  fast  rule. 


Two-Part  Counterpoint 


This  interval  is  also  disagreeably  prominent  when  one  of 
the  notes  forming  it  bears  a  perfect  fifth. 

(a)  (b)  (c)  (d) 

1 


J ,]  I J.  J 


IV    V 

We  are  so  accustomed  in  modern  times  to  the  progression 
from  the  sub-dominant  to  the  dominant  (d)  that  very 
little  objection  can  be  raised  to  it.  Example  (c)  should, 
however,  generally  be  avoided,  and  (a)  and  (b)  introduced 
with  discretion.  When  chords  are  being  combined  which 
contain  the  factors  of  the  tritone,  if  one  of  the  voices  leaps 
a  third,  no  trouble  will  arise.  This  device  will  prevent  the 
roots  of  the  chords,  both  in  the  fundamental  position,  from 
moving  by  step;  for  example. 


fc 

=j=i 

j-j—  J 

—  --, 

h51  i 

B 

/ 

/e 

—  V-  — 

6\ 

=3= 

V 

m 

IV  VIP  vii  °  IV   V  ii 


V 


In  each  of  these  combinations  we  find  the  factors,  f,  b,  in 
successive  chords  and  yet  no  disagreeable  effect  is  felt. 
(Reread  §8  in  Chapter  I.)  By  means  of  the  same  device 
(the  leap  of  a  third)  triads  IV  and  V  may  be  smoothly  com- 
bined; for  example. 


IV    V     V    IV 

§41.  The  best  and  most  usual  cadences  are  the  follow- 
ing: 


best 


possible 


best 


possible 


fe 

w 

6 

^F^ 

-*>• 

-*»- 

6 

Tonal  Counterpoint 


best 


best  possible 


$*= 

6 

6 

•* 

§42.  In  the  exercises  in  the  minor  mode,  to  avoid  the 
augmented  second  the  melodic  form  of  the  minor  scale  is 
to  be  used;  that  is,  the  sixth  and  seventh  degrees  are  to 
be  raised  in  ascending  passages  and  lowered  in  descending. 

§43.  A  few  general  suggestions  are  these:  Avoid  the 
monotony  which  is  the  result  of  motionless  parts  or  tire- 
some repetitions;  on  the  other  hand,  do  not  have  recourse 
to  large,  meaningless  skips.  Successive  wide  skips  in  the 
same  direction  are  invariably  bad;  for  example, 


In  general,  the  motion  should  be  smooth  and  cantabile, 
—  mostly  diatonic.  Strive  constantly  for  melodic  interest 
and  variety.  Let  the  course  of  the  melody  as  a  whole 
show  evidence  of  design.  When  the  subject  will  allow 
of  a  sequential  working  out,  the  effect  is  good.  Modulation 
into  nearly  related  keys  is  often  advisable,  especially  from 
a  minor  to  its  relative  major. 

§44.  A  few  examples  are  worked   out  for  the  student's 
guidance :  * 


A.  *0  %  p 

=3=F 

^ 

=3=~- 

6    j 

n 

^ 

FT1 

Zf 

6 

6    6 

6 

(a) 

l.6(Wn 

6 

6     6 

I^H 

SEE 

S 

.^^ 

FH  —  ^^-"  "-i  —  —*-i  —  •- 

At  (a)  the  octave  is  justifiable,  to  save  another  appearance 
of  the  first  inversion  of  the  dominant,  as  well  as  to  gain 
melodic  range.  At  (6)  a  modulation  into  one  of  the 
related  minor  keys  is  effectively  introduced.  We  now 
treat  in  the  lower  voice  the  same  subject  transposed : 

*  In  this  two-part  writing,  while  the  voices  are  few  and  simple,  a  special  effort 
should  be  made  to  acquire  facility  in  the  use  of  the  alto  and  tenor  clefs. 


Two-Part  Counterpoint 


-f- 

rH" 

—  — 

-~-l 

-p 

m 

s. 

6  6 

,— 

—  _ 

— 

-- 

6__ 

6_ 

1  — 

3 

1 

•> 

—  &  — 

6 

= 

t&z 

F 

3 

M 

Note  the  sequential  form  of  the  counterpoint.     A  subject 
in  the  minor  mode  will  involve  new  points  for  consideration  : 


s 

Ji)  a  f= 

j^- 

r^ 

fr 

^=1=1 

5-S-F 

6 

6 

i 

( 

— 

^ 
6 

6 

6 

6 

= 

6 

*     < 

-*J- 

M^ 

H 

In  this  exercise  a  modulation  must  evidently  be  made, 
for  at  (a)  we  find  a  git  in  a  phrase  the  main  tonality  of 
which  is  A  minor.  The  modulation  into  C  major  really 
began  at  (6).  Whenever  there  is  any  doubt  in  two-part 
writing  as  to  what  harmonies  are  outlined,  it  is  well  to 
separate  the  two  voices  so  as  to  allow  room  for  inner  parts, 
and  then  to  fill  in  the  framework.  The  above 
tested  in  this  wav  would  result  as  follows  : 


exercse 


J 


n 


i 


4 


In  like  manner  the  four-part  harmonic  basis  of  the  second 
exercise  in  §44  is  evidently  this : 


i 


2 


" 


j_^ 


j 


j 


The  same  minor  subject  is  now  placed  in  the  bass  and  a 
counterpoint  written  above : 


66 


Tonal  Counterpoint 


f\ 

_  -p 

~ 

Ui 

(i 

i) 

6 

6 

a 

:>     6 
*=F 

=] 

O 

r 

^r 

f= 

6 

6 

8 

2  ^~~2  —  r 

:£-Jr 

3= 

—  1 

~E 

=t= 

At  (a)  and  at  (6)  the  octaves  evidently  stand  for  the  domi- 
nant in  fundamental  position;  at  (c)  the  necessary  modu- 
lation is  made  into  the  relative  major.  Each  one  of  the 
following  exercises  may  be  worked  with  a  counterpoint 
above  and  below,  by  making  the  proper  transpositions 


of 


EXERCISES 


1.     )     8    JIJ    J 


g 


2   ^t 

Sfe 

p 

=p 

L^J 

a 

F 

^= 

^T— 

^ 

i 


4 


s.^yj 


r^H 

- 

|     |    ^ 

g 

i  • 

—  ± 

—Li 

1  —  1> 

UsJ- 

-^ 

1    o      " 

n 


7.   KTTJ^ 
8. 


rij  r 


i'ii  rrif 


io.> 


['[»  j 


CHAPTER  III 
Two-Part  Counterpoint  —  Second  Order 

§45.  When  in  two-part  writing  the  subject  and  the 
counter-melody  move  in  notes  of  different  value,  we  begin 
a  simple  form  of  composition  of  distinct  musical  worth, 
which  offers  much  scope  for  the  students'  imagination 
and  ingenuity.  The  difference  in  rhythm  is  of  the  greatest 
aid  in  making  the  counterpoint  melodious  in  contrast  to 
the  subject.  In  fact,  the  further  on  we  go,  we  shall  see 
that  the  chief  element  in  good  counterpoint  is  variety  of 
rhythmical  effect.  We  shall  begin  with  counterpoint  of 
the  second  order,  so  called,  or  "  two  notes  against  one,"- 
that  is,  whatever  the  duration  of  the  notes  of  the  subject, 
the  counterpoint  moves  twice  as  fast,  in  quarter  notes 
against  halves,  or  in  eighths  against  quarters,  etc.  The 
recommendations  necessary  to  make  a  beginning  in  this 
form  of  writing  are  few  and  simple;  later  we  shall  exam- 
ine more  carefully  into  some  of  the  finer  distinctions. 
First  there  should  be,  with  few  exceptions,  but  one*  har- 
mony in  each  measure,  formed  by  the  note  of  the  subject 
in  connection  with  the  first  note  of  the  counterpoint.  The 
second  note  of  the  counterpoint  heard  against  the  sus- 
tained subject  furnishes  rhythmic  life  and  variety  without 
the  disturbing  effect  of  a  too-frequent  change  of  harmony. 
As  the  harmonic  outline  must  be  clear,  and  as  the  two 
parts  must  form  as  complete  harmony  as  possible,  obvi- 
ously the  two  notes  together  at  the  first  beat  of  each  meas- 
ure, should  with  few  exceptions  form  a  concord. f  In  a  large 

*  The  most  common  exception  to  this  general  rule  is  where  the  subject  below 
moves  from  the  second  degree  to  the  tonic  and  the  counterpoint  ascends  through 
a.  chord  of  the  sixth  from  the  leading  tone  triad : 


Wx    n~, 

= 

k=N 

1  — 
6 

6 

IV 


i  II      VII1- 


t  We  reserve  for  a  later  paragraph  the  discussion  of  the  question  how  far  the  two 
voices  should  be  treated  merely  as  independent  intervals  or  as  substitutes  for  com- 
plete chords. 


68 


Tonal  Counterpoint 


majority  of  cases  this  will  be  a  major  or  minor  third  or  a 
major  or  minor  sixth;  now  and  then_a  fifth  may  be  used 
jf_it  occurs  naturally  in  the  course  of  a  melodious  phrase 
in  the  counterpoint  and  if  it  is  instantly  followed  by  a 
third  or  sixth.  The  octave  may  also  occasionally  be  used 
at  the  first  of  a  measure,  especially  if  it  stands  for  what 
would  be  in  four-part  writing  a  chord  of  the  sixth  with  a 
doubled  third: 


^ 


i 


1 


pg 


In  regard  to  the  second  note  of  the  counterpoint  by  which 
the  contrast  in  rhythm  is  secured,  there  are  five  varieties 
of  motion,  which  will  be  treated,  as  far  as  it  is  possible,  in 
the  order  of  their  frequency  of  occurrence.  First.  —  The 
second  note  may  be  a  non-harmonic  passing  note,  used 
diatonically  up  or  down  the  scale  between  two  harmony 
notes,  parts  either  of  the  same  harmony  in  different  posi- 
tions, or  of  two  distinct  chords.  The  following  groups 
illustrate  the  most  usual  effects: 

ft  *  *      i         s  s 


/£  n 

=F 

=^= 

—  £- 

n 

*f 

6 

3-T 

6 

6 

6 

x    *»  « 

s 

^P 

t=d 

3E 

LMrJ 

*  1          " 

IV 


The  student  will  carefully  observe  that  passing  notes 
approached  and  left  step  wise,  that  is,  moving  diatonically 
up  or  down,  are  more  available  when  the  subject  skips  ; 
for  example, 


etc. 


Here  the  d  as  a  passing  note  is  questionable  as  the  a  and  c 
together  at  the  beginning  of  the  third  measure  can  outline 


Utf^.^  -1 

i);   a  "  — 

*)•'  i  'A  -  P 

6  * 

i  —  '—**  1  —  i 

- 

—  d— 

Two -Part  Counterpoint 


69 


only  a  six-four  chord  from  the  tonic,  which  implies  a  caden- 
tial  effect  too  early,  or  a  sixth  chord  from  the  third  degree 
which  is  weak.  Second.  —  The  second  note  of  the  counter- 
point may  be  another  note  of  the  same  harmony,  a  fifth 
or  root  after  a  third,  etc.,  outlining  what  is  practically  a 
broken  chord: 

better 


f&F^ 

6* 

f4 

6 

6 

-*>- 

6 

a 

6 

"H"^ 

'      '  "   o 

IV 


IV 


V       VI 


This  device  often  furnishes  the  only  available  second  note, 
for  a  passing  note  (especially  when  the  subject  moves 
step  wise)  which  must  progress  diatonically  up  and  down 
the  scale  will  sometimes  not  leave  us  in  the  right  place  at 
the  beginning  of  the  next  measure.  This  will  be  made 
clear  by  the  following  illustrations: 


fflv 

^g  _ 

• 

n 

(f) 

<r 

) 

J 

- 

^ 

*F 

6 

6 

6 

6 

6 

IV 


rjHM*-^—  |-n 

r^ 

F=^ 

^=^\ 

6 

6 

6 

6 

fj 
6 

^-r.—o- 

*» 

\> 

V  IV  in  ii  I  n    vii" 

Third.  —  The  second  note  may  be  what  is  generally  termed 
an  "  auxiliary  note,"  that  is,  a  note  which  goes  step  wise 
up  or  down  from  a  harmony  note  and  then  returns  to  the 
same  note  at  the  beginning  of  the  next  measure,  where  the 
subject  is  such  as  to  allow  this  combination  as  a  possible  har- 
monic outline.  It  is  obvious  that  this  form  of  motion  can 
be  used  only  where  the  chief  melody  proceeds  by  skips. 
At  best  this  device  should  be  used  sparingly,  as  it  is  open 
to  the  serious  objection  of  having  the  same  note  in  the 


jo  Tonal  Counterpoint 

counterpoint  on  two  successive  strong  beats.  This  makes 
for  monotony  rather  than  variety  of  motion  and  freedom 
of  range.  Some  typical  cases  follow. 


pN= 

* 

: 

Nh 

s 

6 

6 

6  ^ 

6 

* 

i= 

IV 


IV    ii 


In  the  third  measure  of  example  (b)  note  that  there  are 
tu'o  harmonies.  Why  would  it  have  been  unwise  to  use  /I 
instead  of  D  for  the  second  note  of  the  counterpoint  in 
this  measure  ?  If  a  dominant  seventh  were  implied  a  better 
cadence  might  be  made;  that  is, 


fa 

$— 

6  * 

vn«    V; 

Fourth.  —  The  rhythm  of  two  notes  in  the  counter- 
point against  one  in  the  subject  may  be  secured  by  revers- 
ing the  usual  order  and  having  the  dissonant  note  strike 
on  the  first  beat  of  the  measure  in  connection  with  the  sub- 
ject, and  be  instantly  followed  by  a  harmony  note  one  step 
up  or  down.  This  note  is  called  an  "  accented  passing  " 
note,  and  as  for  its  origin  it  is  practically  a  lengthened  out 
appoggiatura,  or  grace  note.  In  its  effect  it  is  the  exact 
opposite  of  the  normal  variety  of  passing  note,  which  is  a 
a  note,  more  or  less  dissonant,  occurring  on  a  weak  beat  in 
diatonic  succession  up  or  down  between  two  harmony  notes : 


|JU..     ^ 

rft 

* 

t 

1  —  | 

F^Frl 

* 

i1^ 

H4 

^= 

it 

^ 

"" 

(b) 

In  this  way  the  counterpoint  may  often  be  made  to  flow 
very  smoothly  and  the  accented  dissonances  give  character 


Two-Part  Counterpoint 


and  distinction  to  the  melody.  In  example  (b),  quoted 
from  Cherubini,  the  first  note  D  of  the  second  measure  is  an 
accented  passing  note.  The  harmony  of  this  measure  is  the 
minor  triad,  on  the  sixth  degree,  a,  c,  e,  but  if  either  c  or 
e  had  been  tried  as  the  first  note  of  the  measure  not  only 
would  the  very  effective  ascending  scale  passage  have  been 
sacrificed,  but  it  would  have  been  difficult  to  write  even 
clear  grammar,  as  will  be  seen  from  the  following  attempts : 


riJ-qA-i 

o 

I—:  1 

M  —  1 

Kfo  5  g)  J 
g»  8=3 

5 

S 

s 

(• 

^P 

/"**" 

Here  at  examples  (a)  and  (6)  the  skips  in  the  counterpoint 
are  by  no  means  good,  while  at  (c)  the  grammar  is  posi- 
tively bad  on  account  of  the  consecutive  fifths  between  two 
successive  beats.  (This  point  will  be  more  fully  explained 
later.) 

§46.  Although  modern  counterpoint  implies  the  union  of 
a  definite  harmonic  system  — fixed  scales  and  a  clear  tonality 
—  with  true  contrapuntal  style,  —  that  is,  the  independent 
and  characteristically  melodious  progression  of  each  part, — 
we  must  see  to  it  that,  in  striving  for  this  union,  our  coun- 
terpoint does  not  degenerate  into  mere  rhythmically  ani- 
mated harmony.  At  first,  to  be  sure,  the  student  has  to 
pay  rather  too  much  attention  to  the  harmonic  outline, 
but  as  soon  as  he  can  carry  on  subconsciously,  as  it  were, 
a  simple  and  natural  harmonic  scheme,  all  his  attention 
should  be  centered  upon  the  life  and  independent  charac- 
ter of  each  of  the  contrapuntal  voices.  Nothing  conduces 
more  toward  this  end  than  a  frequent  and  liberal  use  of 
accented  passing  notes.  In  this  way  the  writing  is  freed 
from  obvious  and  tame  harmonic  construction,  and  a 
stimulating  pungency  and  variety  is  secured  for  the  style. 
In  the  following  passage  from  "  Cosi  fan  tutte  "  it  is 
instructive  to  observe  that  Mozart  in  treating  contra- 
puntally  the  simple  chords  of  C  and  F  writes  as  follows: 


Tonal  Counterpoint 


that  is,  accented  passing  notes  are  introduced  instead  of  a 
tame  harmonic  circumscription  as  follows: 


Little  by  little  the  student  should  systematically  avoid  a 
counterpoint  which  is  merely  a  rhythmic  transformation  of 
what  the  natural  harmony  would  be  in  outline;  for  example, 


£ 


m 


For  example,   suppose  we  wish  to  write  a    counterpoint 
of  the  second   order  below  the  following  simple  melody: 


ii 


7Ti  r  i'  r  i  J  i'  r  i  "• 


If  harmonic  background  were  all  that  it  is  necessary  to 
consider,  the  following  would  be  a  satisfactory  version : 


1 

JrTrr 

1 

M 

^ 

L  —  

Jn  i  r1 

i 

-i— 

N^ 

—  P  —  ' 

But  considered  as  counterpoint  this  lower  voice  is  dis- 
jointed in  style  and  very  tame  in  character.  In  the  fol- 
lowing version  the  counterpoint  is  made  far  more  inter- 
esting by  the  introduction  of  accented  passing  notes. 


f£-T- 

1  r>    |g 

PP= 

P  P  i 

^^=W 

fe 

* 

=1 

* 

F^4=t 

c  •* 

m? 

Tl  '  '  1  '  ^'^ 

4= 

h 

t  —  *-"  —  u 

In  the  second  and  third  measures  observe  in  particular 
the  independence  of  the  ascending  diatonic  passage  which 


Two-Part  Counterpoint 


73 


cuts  its  way,  as  it  were,  through  the  harmonic  tissue. 
Above  all,  the  earnest  student  should  play  and  thoroughly 
analyze  certain  of  the  works  of  Bach,  —  especially  the 
forty -eight  Preludes  and  Fugues,  the  two-voice  Inventions 
and  some  of  the  Chorals  and  Cantatas.  These  composi- 
tions represent  the  most  perfect  union  of  a  free  contra- 
puntal style  with  our  modern  harmonic  system.  A  few 
suggestive  examples  are  cited: 

BACH.     Fugue  No.  i 


^tr 


BEETHOVEN.     String  Quartet,  Op.  18,  No.  4 


BACH.     2d  Fugue.    "  Well-Tempered  Clavichord  " 


74 


Tonal  Counterpoint 


Fifth.  —  The  second  note  may  be  what  is  called  a  "  chang- 
ing note."  This  is  the  least  used  of  all  the  devices,  though 
for  variety  it  is  occasionally  of  good  effect.  When  we 
come  to  the  next  order  (four  notes  against  one)  we  shall 
analyze  more  fully  this  form  of  motion.  A  changing  note 
is  a  dissonant  note  on  the  weak  part  of  the  measure  from 
which  a  skip  of  a  third  is  made  in  the  opposite  direction. 
The  next  note  must  almost  invariably  be  the  note  within 
the  skip,  otherwise  the  ear  is  by  no  means  recompensed 
for  the  temporary  change  of  direction.  For  instance, 
suppose  that  from  an  f,  as  the  first  note  in  a  measure  of 
counterpoint  two  against  one,  we  proceed  to  g;  for  the 
following  note  the  ear  unconsciously  and  yet  with  perfect 
reason  expects  either*  an  a  (in  this  case  the  g  is  a  simple 
passing  note)  or  another  f  (the  g  now  being  treated  as  an 
auxiliary  note).  After  the  g  our  ear  will  also  tolerate  an 
e,  a  skip  of  a  third  in  the  opposite  direction  from  which 
we  started,  provided  that  the  next  note  is  an  f.  Treated 
in  this  way  the  e  is  a  kind  of  interpolated  note,  or  one 
which  merely  delays  the  logical  direction  of  the  counter- 
point. A  common  example  will  make  all  this  plain: 


^ar  rTi'  rf  ,-• 

f—r- 

6 

6 

=*= 
6 

6 

2 

No  mistake  is  more  common  in  the  use  of  "  changing 
notes  "  than  to  forget  that  of  the  group  of  four  notes  the 
last  must  invariably  return  within  the  skip  of  the  third. 

Cases  are  found,  to  be  sure,  of  what  may  be  called  "  single  changing   notes  "; 
for  example, 

MOZAI'T      Rondo  in  A  minor 


HANDEL.     "Messiah,"  Mo.  23 


r    r 


f 


The  student,  however,  should  not  use  this  device  too  often  until  he  has  acquired 
facility  in  the  more  normal  use  of  changing  notes  in  pairs, — that  is,  one  on  each 
side  "f  the  harmony  note. 


Two-Part  Counterpoint 


75 


Where  this  is  not  done,  an  effect  of  aimlessness  is  often 
produced  which  is  most  disturbing.  The  melody  seems, 
as  it  were,  to  fly  off  "  at  a  tangent."  Such  combinations 
as  the  following  are  obviously  very  unmelodic: 


§47.  In  all  contrapuntal  writing  great  care  must  be 
taken  to  have  the  harmony  logical  and  natural  from  one 
chord  to  another, — that  is,  between  the  accented  beats-  of 
successive  measures.  Fifths  and  octaves  therefore  in 
these  places  are  not  justified  by  intermediate  notes  on  the 
•unaccented  beats;  for  example, 


bad 


bad 


Between  consecutive  unaccented  notes,  however,  or  even 
between  an  unaccented  and  an  accented  note,  perfect 
fifths  and  octaves  are  allowable  whenever  it  is  evident  that 
no  false  harmonic  connection  is  implied;  for  example,  no 
objection  can  be  made  to  any  one  of  the  following  passages : 


(fr)§  ? 

1 

"^ 

3 

- 

F^ 

|    Jc/c.||J    j 

- 

—  J  1  g 

^ 

J 

TF- 


As  to  combinations  involving  an  unaccented  and  an 
accented  note  the  test  of  good  or  bad  harmony  should 
invariably  be  applied ;  for  example,  the  following  measures 

are  bad,  as  the  implied  harmony    is  evi- 
dently this: 


j6  Tonal  Counterpoint 

on  the  other  hand,  this  progression 


is  perfectly  allowable,  as  the  implied  harmony 
will  prove: 


§48.  When  the  counterpoint  is  below  the  subject,  sec- 
ond inversions  should  seldom  be  implied.  It  is  evident 
that  a  six-four  chord  is  outlined  when  the  third  is  in  the 
subject  and  the  counterpoint  descends  from  the  root  to 
the  fifth  of  the  same  chord;  for  example, 


This  effect  is  not  absolutely  forbidden;  no  objection  can 
be  found  to  the  following  counterpoint: 


P5" 

ffi 

— 

•"•—  -^ 

* 

^^ 

-  f  1 

^= 

I    rj 

=M 

and  in  actual  music  it  is  largely  a  matter  of  speed  whether 
second  inversions  shall  be  outlined  or  not.  At  a  slots 
tempo  there  is  no  doubt  that  a  frequent  use  of  six-four 
chords  renders  the  counterpoint  weak  and  halting;  for 
example,  the  following  passage  would  be  very  bad: 


6 
4 

'   1      o 

l=£= 

At  a  rapid  tempo,  however,  where  the  effect  of  any  particu- 
lar harmonic  outline  is  but  momentary,  the  above  objec- 


Two-Part  Counterpoint 


77 


tion  is  greatly  modified.  Mozart,  for  instance,  in  the 
first  of  his  charming  "  Duos  "  for  Violin  and  Viola  has 
the  following  passage: 


In  general,  however,  until  the  student  has  acquired  a  sure 
judgment,  the  counterpoint,  when  it  is  in  the  lower  part 
should  not  descend  to  the  fifth  of  the  chord.  There  is  no 
objection  to  the  counterpoint  rising  from  the  root  to  the 
fifth,  or  falling  from  the  fifth  to  the  root;  for  example, 


for,  as  the  ear  accepts  the  lower  of  two  notes  as  the  real 
bass,  in  each  of  these  cases  the  fundamental  position  of 

the  chord  is  outlined,  —  that  is, 


§49.  As  it  is  our  aim  to  make  the  counterpoint  as 
smooth  and  flowing  as  possible,  when  the  exercises  are  in 
the  minor  mode,  the  augmented  second,  found  between  the 
sixth  and  seventh  degrees  of  the  harmonic  minor  scale, 
should  seldom  be  employed.  We  use  therefore  as  passing 
notes  the  major  sixth  and  the  minor  seventh,  the  former 
between  the  dominant  and  the  leading  tone;  for  example, 


Tonal  Counterpoint 


and  the  latter,  the  minor  seventh,  in  descending  or  ascend- 
ing phrases  between  the  sixth  degree  and  the  tonic;  for 
example, 


Note  carefully  that  in  all  the  above  examples  the  ajl  and 
the  bl>  are  used  as  passing  notes  on  the  weak  part  of  the 
measure,  never  as  harmony  notes;  that  is,  the  subdomi- 
nant  harmony  in  the  key  of  C  minor  should  invariably  be 


C:    IV 


and  in  like  manner  the  dominant  harmony 


C:    V 


The  only  apparent  exception  to  this  principle  is  seen  in 
example  (a)  above  in  this  paragraph,  in  the  next  to  the 
last  measure.  Here  the  ajl  is  an  accented  passing  note 
used  diatonically  before  b  R.  ,  and  the  harmony  implied  is 
the  first  inversion  of  the  leading  tone  triad.  The  above 
statements  are  not  meant  to  be  comprehensive;  in  free 
writing  for  pianoforte  and  strings,  the  minor  scale  is  capa- 
ble of  great  variety  in  its  treatment,  as  may  be  seen  from 
an  analysis  of  the  works  of  Bach,  of  Handel  and  of  others; 
for  example, 

HANDEL.     "Judas  Maecabaeus,"  No.   17 


Two-Part  Counterpoint 


79 


BACH.    "  S.  Matthew  Passion,"  No.  10 


In  general,  however,  it  is  best  in  the  minor  mode  to  use  for 
the  counterpoint  the  melodic  form  of  the  scale;  that  is, 
to  raise  the  sixth  and  the  seventh  degrees  in  ascending 
passages  and  to  lower  them  in  descending;  for  example, 


BACH.     4th  Prelude 


^•TOfflCTaffEJiife 


§50.  The  best  forms    of   cadences    in  this  order  are  the 
following : 


TT      -®" 


f 


§51.  A  few  examples  are  now  worked  out  as  models  for 
the  student: 


6       6 


& 


I         IV      a  I 


(a) 


S^ 


So 


Tonal  Counterpoint 


In  the  second  rather  smoother  version  observe  at  (a)  the 
mediant  triad  in  the  fundamental  position,  followed  by 
the  triad  on  the  sixth  degree;  always  an  effective  combi- 
nation. At  (&)  we  have  two  harmonies  against  one  note 
of  the  subject.  A  counterpoint  is  now  placed  below  the 
same  subject  transposed: 


$  s 

—  H 

-H  |- 

•'  J 

^=p= 

-rf-7*- 

3 

—  I  —  (- 

1   1 
=riS= 

.  i  i 

&m 

Wm 

& 

(I  VI) 

Observe  the  effective  use  of  the  accented  passing  note  at 
(a).  In  this  form  of  writing  (two  notes  against  one)  it  is 
often  extremely  difficult  to  outline  natural  harmony  and 
yet  make  the  counterpoint  flow  smoothly.  Frequently  the 
introduction  of  an  accented  passing  note  is  the  very  means 
of  avoiding  too  many  successive  skips  and  of  securing  an 
independent  design  for  the  counterpoint.  In  this  case, 
for  instance,  we  secure  a  diatonic  phrase  of  nearly  an 
octave.  The  same  subject  with  counterpoint  above: 


Simple  as  this  exercise  is,  note  at  (a)  how  effectively  the 
climax  in  the  counterpoint  has  been  saved  for  the  fifth 
measure  where  the  opening  notes  of  the  subject  are  re- 
peated. Although  the  counterpoint  is  very  smooth,  from 
an  artistic  point  of  view  the  general  effect  is  rather  tame, 
that  is  the  harmonic  background  is  rather  too  evident. 
A  more  characteristic  counterpoint  could  be  made  by  the 


Two-Part  Counterpoint 


81 


systematic  introduction  of  accented  passing  notes  as  fol- 
lows : 


At  (a)  observe  the  accented  passing  note  approached  by 
the  leap  of  a  third  in  contrary  motion  to  the  bass. 

§52.  We  now  write  two  counterpoints  to  a  short  melody 
in  the  minor  mode; 


6      fa;  6 


the  second  measure  illustrates  the  usual  treatment  of  the 
minor  scale  in  the  contrapuntal  voice:  at  (a)  the  major 
sixth  is  used  effectively  as  an  accented  passing  note. 


KM  i\>Lrrr= 

»rrrrCJ 

|     —  —  j  —  i^  — 

1  —  L  '    |  _j  — 

(a) 

7    fc  4    -  —  \—  3  
s 

B  —  r  r  i 

[_p_J  f_J 

1  r 

By  the  use  of  two  successive  accented  passing  notes  in  the 
first  measure  we  start  the  counterpoint  with  a  flowing 
phrase.  Let  the  student  ask  himself  what  harmony  is 
outlined  by  the  octave  at  (a).* 

*  Hi  attempting  to  work  out  the  exercises  in  this  order,  the  student  must  con- 
stantly bear  in  mind  that  he  is  not  to  follow  these  rules  in  a  merely  mechanical 
manner,  but  to  use  them  towards  the  cultivation  of  a  well-trained  instinct  for 
effective  melody  formation  (see  paragraphs  19  to  23,  Chapter  I).  Unless  this 
suggestion  is  borne  in  mind  the  exercises  are  apt  to  degenerate  into  a  set  of 
"puzzles  "  without  any  real  melodic  life  or  interest,  and  of  no  musical  value.  It 
should  be  understood  that  certain  of  these  exercises  are  nothing  more  than  exer- 
cises as  far  as  lasting  musical  value  is  concerned.  In  order  to  improve  his  gram- 
matical knowledge  of  music,  the  student,  however,  must  not  shirk  them  any  more 
than  a  person  learning  the  pianoforte  would  forego  certain  technical  exercises  of 
a  purely  gymnastic  nature,  or  an  athlete  would  think  of  doing  without  certain 
routine  mechanical  tests.  On  the  other  hand  he  must  try  to  make  them  as  inter- 
esting and  varied  as  his  somewhat  limited  skill  will  allow.  He  will  be  richly  repaid 
for  all  his  pains  when  he  comes  to  free  contrapuntal  writing,  namely,  four-part 
songs,  simple  movements  for  string  quartet,  inventions  for  pianoforte,  etc.  Then 
with  a  quickened  imagination  and  a  trained  judgment  he  may  do  work  of  permanent 
artistic  worth. 


82 


Tonal  Counterpoint 
EXERCISES 


The  first  six  subjects  should  be  worked  out  with  a  counter- 
point both  above  and  below,  the  proper  transposition  of 
key  being  made  in  each  case. 


5    9;i>!l_L 

jjjj 

F^T 

i  p  • 

=^ 

br:F 

HI 

^N 

i 

T'  r 

L^ 

Us 

i 


s 


§53.  Several  longer,  more  periodic  melodies  are  now 
given.  They  are  freer  in  style  and  will  afford  considerable 
opportunity  for  the  ingenuity  and  good  taste  of  the  stu- 
dent. The  version  worked  out  should,  as  far  as  possible, 
be  tested  by  actual  performance.  The  notes  on  paper 
are  mere  symbols,  and  often  that  which  looks  very  plausi- 
ble when  written,  sounds  quite  different. 

§54.  Before  these  exercises  are  begun  the  student  should 
endeavor  to  widen  his  conception  of  the  term  Interval.  In 
the  first  weeks  of  contrapuntal  study  a  rather  undue  stress 
has  to  be  laid  upon  intervals  as  the  outlines  of  definite 
chords,  in  order  that  a  clear  harmonic  background  may  be 
established.  Gradually,  however,  we  should  understand 
that  the  independent  individuality  of  a  counterpoint  may 
justify  the  free  introduction  of  intervals  which  in  mere 
harmonic  combinations  would  be  unnatural,  if  not  posi- 
tively incorrect.  In  regard  to  fifths  and  fourths  for  ex- 
ample, a  free  use  of  these  intervals  as  mere  intervals  often 
conduces  to  a  boldness  and  vigor  in  the  counterpoint 
otherwise  unattainable.  A  few  examples  from  the  "  Well- 
Tempered  Clavichord  "  of  Bach  will  make  this  clear: 


Two-Part  Counterpoint 

Fugue  No.  5.  sd  Book 


£ 


* 


Fugue  No.  12.  ad  Book 


In  this  connection  it  is  well  to  remind  the  student  that  at 
times  between  certain  voices  there  may  be  parallel  fifths 
to  which,  on  account  of  the  passing  character  of  the  notes 
or  the  melodic  independence  thereby  gained,  no  gram- 
matical objection  can  be  made.  This  is  illustrated  by  the 
well-known  passage  from  Mozart's  "  Magic  Flute  "  over- 
ture : 


84  Tonal  Counterpoint 

We  find  likewise  that  the  dissonant  intervals  of  the  second 
and  the  seventh,  though  generally  to  be  introduced  as 
suspensions  (with  strict  or  free  resolutions)  are  capable 
of  free  treatment  which  shall  make  for  individuality  and 
variety  in  the  counterpoint. 

Examples  of  the  Interval  of  the  second: 


Examples  of  the  Interval  of  the  seventh : 
f.# 


f  r  r  T 


A/^.    S.  —  All    the    above    examples    should    be    played 
through  carefully  and  committed  to  memory. 

MELODIES 


Two-Part  Counterpoint 


2. 


».«?.    same  as  above  subject 
transposed  into (f& Major. 


5. 


=£=* 

=3= 

.,[.  ..!_.. 

H- 

=P= 

L'r 

^ 


r    r      r 


6. 


i 


For  the  continuation  of    Xos.  5   and   6    see   Chapter  I, 
Soprano  melodies  Nos.  9  and   10.  p.  52. 


CHAPTER    IV 
Two-Part  Counterpoint  —  Third  Order 

§55.  We  now  attempt  the  formation  of  a  contrapuntal 
part  which  shall  move  four  notes  against  one  in  relation 
to  the  chief  melody  or  subject.  Beginning  with  this  type 
of  writing,  the  exercises,  even  those  which  are  somewhat 
formal,  will  afford  the  student  opportunities  to  make  his 
melodies  more  flowing  in  character  and  more  varied  in 
design;  hence  his  work  will  become  far  more  interesting. 
The  devices  for  securing  motion  are  largely  the  same  as 
those  studied  in  the  preceding  chapter,  except  with  a 
wider  and  freer  application.  In  this  order  the  notes  of 
the  counterpoint  are  so  selected  that  we  have  either  one 
or  often  two  harmonies  in  each  measure.  If  a  single  har- 
mony, it  will  be  outlined  by  the  first  note  of  the  counter- 
point in  connection  with  the  subject  note,  and  the  three 
remaining  notes  will  be  a  mixture  of  notes  of  the  same 
chord,  passing  notes  and  auxiliary  notes,  with  now  and 
then  an  accented  passing  note  interspersed.  If  there  is 
to  be  a  second  harmony  in  the  measure,  the  change  should 
almost  always  be  made  with  the  third  note  of  the  counter- 
point, that  is,  on  the  secondary  accent,  and  very  seldom 
at  the  second  or  the  last  note  of  the  group  of  four. 


In  the  above  examples  at  (a)  we  see  two  passing  notes, 
one  unaccented  and  one  accented,  between  two  harmony 
notes;  the  fifth  and  the  octave  of  the  root.  At  (b)  we  see 
the  triad  outlined  with  root,  third  and  fifth  and  an 
accented  passing  note  interspersed.  At  (c)  we  have  two 
passing  notes;  (d)  is  like  (b);  (c)  shows  a  single  passing 
note,  and  (/)  an  auxiliary  note.  It  is  well  for  us  at  this 
point  to  part  company  with  "  vocal  counterpoint  "  in  the 
literal  meaning  of  the  term,  that  is,  in  the  sense  that  we 
imagine  the  exercises  to  be  executed  invariably  by  voices. 
The  writing,  however,  should  not  cease  to  be  "vocal  "  in 
spirit,  that  is,  flowing  and  cantabile,  although  the  parts 


86 


Two-Part  Counterpoint  8j 

may  have  a  wider  range  and  move  at  a  greater  speed  than 
would  be  effective  for  execution  by  the  human  voice.  A 
great  many  passages  in  the  pianoforte  writings  of  Bach 
or  in  the  string  quartets  of  Haydn,  Mozart  and  Bee- 
thoven, barring  the  mechanical  limitations  of  range,  breath 
and  speed,  can  be  thought  of  as  executed  by  ideal  human 
voices,  so  truly  vocal  is  their  spirit  and  so  smooth  and 
homogeneous  the  harmonic  connection.  Furthermore, 
in  all  composition,  simple  or  complex,  strictly  meant  for 
voices  the  words  have  to  be  taken  into  account,  and  in 
counterpoint  of  four  notes  against  one  it  is  difficult,  ex- 
cept in  florid  colorature  writing,  to  imagine  syllables  mov- 
ing effectively  at  such  a  speed  for  any  long  period.  The 
following  exercises,  therefore,  are  designed  in  general  for 
strings  and  for  pianoforte.  As  the  forms  of  melodic  outline 
are  so  varied  in  this  order,  it  will  be  well  for  the  student  to 
begin  with  certain  definite  rules,  and  he  is  strongly  recom- 
mended to  analyze  carefully  the  examples  submitted. 
.  §56.  In  the  opening  measure  of  an  exercise  the  first 
beat  of  the  counterpoint  should  be  a  rest  and  the  first 
note  a  perfect  concord  —  an  octave,  fifth,  or  rarely  a  unison. 
(The  unison  is  better  on  strings  when  each  note  is  actually 
taken  by  a  separate  instrument  than  on  the  pianoforte 
where  the  same  single  key  has  to  do  two  different  things 
at  once.)  The  remaining  two  notes,  that  is,  the  third  and 
fourth  beats,  may  be  treated  in  various  ways;  one  may 
be  another  factor  in  the  harmony  already  outlined  and  the 
fourth  a  passing  note ,  or  they  may  both  be  passing  notes ; 
or  one  may  be  an  auxiliary  note,  or  often  an  accented  pass- 
ing note.  It  is  better  not  to  have  all  three  outline  the 
same  harmony;  for  example. 


This  in  general  is  not  desirable  for  the  first  measure.  In 
fact,  throughout  this  order  the  arpeggio  of  a  chord  is  gen- 
erally rather  weak,  although  not  absolutely  prohibited, 
especially  in  counterpoint  for  pianoforte.  Here  follow 
some  examples  of  first  measures  illustrating  the  above 
considerations : 


88 


Tonal  Counterpoint 


pmi 

6 

*):|lf  j 

6 

i« 

iy  **Jni 

•'*+*}  1  1 

P 

1  lc£d 

L4  —  1  |  !  1 

5 

IV 


In  the  measures  between  the  first  and  last,  this  group  of 
four  notes  is  generally  a  combination  of  harmony  notes, 
passing  notes,  accented  passing  notes  and  auxiliary  notes. 
Only  practice  and  the  gradual  cultivation  of  an  instinct 
for  melody  formation  will  enable  the  student  to  make  his 
counterpoint  both  grammatical  and  of  independent  inter- 
est. In  order  to  help  him  to  this  end  a  few  general  recom- 
mendations will  be  given,  and  certain  methods  carefully 
analyzed.  In  this  order  of  counterpoint  our  chief  aim 
should  be  to  make  the  secondary  melody  flow  smoothly; 
on  the  other  hand,  it  must  not  become  tame  by  the  con- 
stant use  of  the  same  notes,  or  by  the  recurrence  of  the 
same  figure;  for  example, 


i 


Two-Part  Counterpoint 


89 


In  this  example  we  see  the  weakness  and  monotony  of  a 
too  frequent  recurrence  of  the  same  designs.  Although  the 
material  is  very  simple  at  first,  the  student  should  always 
try  to  make  the  counterpoint  express  as  much  as  possible. 


Ex.  i 


Ex.  2 


" 


In  Example  i,  no  neglect  of  the  ordinary  rules  can  be 
found,  save  the  suspension  at  (a)  introduced  diatonically 
instead  of  by  a  leap  (this  point  will  be  explained  later), 
and  yet  the  writing  is  very  stiff  and  monotonous.  Let  the 
student  play  over  Example  2  and  he  will  see  at  once  how 
much  freer  is  the  range  of  the  counterpoint  and  how  much 
greater  its  life  and  variety.  Notice  that  although  in  gen- 
eral skips  should  be  avoided,  occasional  skips  of  fourths, 
fifths  and  octaves  give  vigor  and  interest  to  the  melody. 

$57.  In  nothing  is  the  student  more  likely  to  go  wrong 
than  in  his  treatment  of  passing  notes.  He  either  uses  pass- 
ing notes  which  do  not  "  pass  "  or  the  notes  imply  a  change 
of  harmony  on  the  weak  parts  of  the  group,  the  second 
and  fourth  notes.  This  will  be  clear  from  the  following 
examples : 

(a)  (b)  (c) 


f^~fT 

-—  — 

^-a-i 

#= 

tp 

= 

1    ^     |       1       1     II 

"i  6 

-4= 

«F= 

Here  in  example  (a)  the  second  and  third  notes  b  and 
g  are  illogical;  if  b  is  a  passing  note  it  cannot  be  left 
by  skip;  and  if  a  harmony  note  it  makes  the  change  at 
the  iveak  part  of  the  measure.  The  same  considerations 


go  Tonal  Counterpoint 

apply  to  the  f  and  b  in  example  (b),  and  to  the  a  and  c  in 
example  (c).  Let  us  then  bear  firmly  in  mind  two  leading 
principles:  First,  in  general  it  is  best  to  have  but  one 
iiarmony  in  each  measure;  if  occasionally  two  are  used, 
the  change  must  always  be  made  at  the  third  note  of  the 
group  of  four.  Second,  passing  notes  must  invariably  be 
approached  and  left  by  steps,  and  must  pass  on  in  the 
same  direction  in  which  they  started.  Compare  carefully 
the  right  and  wrong  use  of  the  two  passing  notes  in  the 
following  examples: 

(a)  bad  (ft)  bad  (c)  good  (d)  good 


j«i**idii  ^**^ 


In  all  these  cases  a  and  b  are  passing  notes,  but  in 
the  first  two  examples  they  do-  not  proceed  in  the  same 
direction,  and  also  imply  a  change  of  harmony  at  the 
wrong  place.  In  examples  (c)  and  (d)  these  faults  are 
remedied.* 

§58.  In  this  order  of  counterpoint  a  judicious  use  of 
changing  notes  gives  interest  and  variety  to  the  melodies. 
As  the  student,  however,  often  makes  a  wrong  use  of  these 
notes,  it  will  be  well  to  explain  a  little  more  fully  their  real 
nature.  In  a  group  of  four  notes,  let  the  first  two  notes 
be  c,  d;  as  c  and  d  obviously  cannot  belong  to  the  same 
harmony,  the  d  must  either  be  a  passing  note  (in  which 
case  the  following  note  must  be  e)  or  an  auxiliary  note 
(in  which  case  an  instant  return  must  be  made  to  c  for  the 
third  note).  But  if  instead  of  either  of  these  two  modes 
of  progression,  a  skip  of  a  third  is  made  in  the  opposite 
direction  from  the  start  and  then  an  instant  return  made 
to  the  note  within  the  third,  these  two  auxiliary  notes  on 
either  side  of  the  harmony  note  are  called  changing  notes ; 
that  is, 


In  these  examples  the  d  and  b  are  changing  notes  and  in  each 
case  a  return  is  made  for  the  fourth  note  to  the  one  lying 
within  the  skip  of  a  third.  Simple  as  this  is  in  theory, 
there  are  right  and  wrong  ways  of  using  this  device 
in  actual  practice;  so  that  a  few  more  suggestions  may 

*  Figures  like  those  criticised  may,  it  is  true,  sometimes  be  found  in  rapid  pas- 
sages for  the  violin,  but  in  general  the  student  will  do  well  to  follow  the  recom- 
mendation laid  down. 


Two-Part  Counterpoint 


91 


may  prove  helpful.  First,  when  changing  notes  are  to  be 
used  they  should  appear  as  the  second  and  third  of.  the 
groups  of  four  and  not  as  the  third  and  fourth. 


not  good 


Secon-d,  the  student  is  often  in  doubt  as  to  whether  the 
higher  or  lower  of  the  two  changing  notes  should  come 
first,  that  is,  whether  his  group  should  be  a  or  b. 


This  point  is  settled  by  looking  forward  to  the  next  note 
of  the  subject  and  planning  the  group  so  that  the  note  in 
the  counterpoint  which  must  be  used  on  the  first  note  of 
the  second  measure  is  not  anticipated  on  the  preceding 
secondary  accent;  that  is, 


i 


In  both  (a)  and  (b)  the  first  note  of  the  counterpoint  in  the 
second  measure  (required  by  the  note  of  the  subject)  is 
anticipated  by  the  note  on  the  secondary  accent  of  the 
measure  preceding.  This  gives  an  effect  of  weak  monotony. 
The  remedy  is  in  each  case  to  start  the  changing  note  in 
just  the  opposite  direction.  -Compare  carefully  (c)  and  (d) 
with  (a)  and  (b)  above. 


Third,  it  is  seldom  advisable  to  use  changing  notes  so  that 
a  leap  to  an  accented  note  is  preceded  by  a  step  in  the 
same  direction;  that  is,  in  examples  (a)  and  (b)  the  com- 
binations of  notes  d,  c,  a,  and  b,  c,  e,  are  disjointed  and 
unmelodic. 


gz  Tonal  Counterpoint 

By  grouping  the  changing  notes  as  in  examples  (c)  and 
(d)  below  we  make  the  counterpoint  far  more  symmetrical 
and  melodious. 


A  few  examples  are  cited  from  standard  compositions : 

HANDEL.    "Messiah,"  No.  12 


BACH.    Well-Tempered  Clavichord.     2d  Book.  Fugue  I 


This    whole    fugue    abounds    in    interesting    contrapuntal 
devices  and  will  repay  careful  analysis. 


Both  examples  from  CHOPIN.    Op.  10,  No.  4 


As  little  by  little  facility  is  acquired  in  writing  counter- 
point of  four  notes  against  one,  it  will  be  evident  that  the 
general  principle  that  a  passing  note  may  be  interrupted 


Two-Part  Counterpoint 


93 


in  its  progression  is  capable  of  very  broad  interpretation. 
In  all  contrapuntal  composition  figures  like  the  following 
are  to  be  seen:  * 


Groups  of  changing  notes  which  make  with  the  subject  the 
interval  of  the  diminished  octave  give  distinction  to  the 
counterpoint  and  this  effect  should  occasionally  be  intro- 
duced; for  example, 

.* 


A  beautiful  example  of  an  analogous  effect  (a  single  auxil- 
iary note  introduced  by  leap  of  a  third)  is  seen  in  the 
"Recordare"  of  Mozart's  Requiem: 


In  the  last  measure,  note  the  striking  poignant  effect  of  the 
Bi>  .against  the  Btt.  See  also  the  following  passage  from 
the  second  movement  of  Beethoven's  Sonata,  Op.  28: 


The  whole  last  part  of  this  movement  should  be  carefully 
analyzed  by  the  student. 

*  Experience  has  convinced  the  writer  that  it  is  unwise  at  this  stage  to  burden 
the  student  with  too  many  rules.  It  is  left  for  the  teacher  to  keep  pace  with  his 
development  and  to  show  him  from  actual  examples  how  freely  some  of  the  rules 
mav  be  modified. 


94 


Tonal  Counterpoint 


In  free  writing  for  pianoforte  or  strings,  auxiliary  notes 
are  often  taken  by  leap,  although  they  are  generally  left 
diatonically  even  in  the  freest  style.  A  very  instructive 
passage  is  cited  from  von  Weber's  "  Invitation  to  the 
Waltz": 


In  the  third  and  fourth  measures  we  find  accented,  and  in 
the  seventh  and  eighth  unaccented,  auxiliary  notes  grouped 
around  the  tonic  chord.  The  student  is  strongly  urged 
not  to  make  a  frequent  use  of  changing  notes  of  any  kind, 
until  he  has  acquired  a  very  sure  instinct  for  knowing  just 
what  effect  he  wishes.  His  counterpoint  should  consist 
largely  of  passing  notes,  auxiliary  notes,  and  now  and  then 
of  an  arpeggio  of  the  main  harmony.  Accented  passing 
notes  on  the  third  beat  of  the  group,  or  even  on  the  first, 
may  systematically  be  introduced.  The  slight  discord 
occasioned  by  their  use  gives  interest  and  vigor  to  the 
counterpoint,  and  they  are  often  very  useful  in  preserving 
a  uniform  diatonic  progression;  for  example, 


§59.  In  working  out  exercises  in  the  minor  mode  the 
student  is  reminded  of  the  general  considerations  already 
noted  (Chapter  III,  §49)  in  regard  to  the  sixth  and  sev- 
enth degrees.  In  counterpoint  of  this  order,  with  its  gen- 


Two-Part  Counterpoint 


95 


erally  rapid  tempo,  the  augmented  second  found  in  the 
harmonic  scale  is  usually  avoided  by  raising  both  the 
sixth  and  seventh  degrees  in  ascending  passages,  and  lower- 
ing them  in  descending;  that  is, 


They  are  also  available  as  changing  notes,  as  may  be  seen 
from  the  following  figures: 


^ 


Occasionally  in  a  descending  passage  the  minor  seventh 
may  be  used  as  a  harmony  note.  In  this  case,  except 
where  a  passing  modulation  into  the  relative  major  is  dis- 
tinctly implied,  the  first  note  in  the  counterpoint  of  the 
following  measure  should  generally  be  the  sixth  degree. 


C  minor 


I/!,",  A.. 

P 

.   ^    ^     if  1  = 

t 

=^ 

1 

\r   ^  l>  4  n  1 

1  

I  —  F= 

r^z^d 

§60.  A  very  clear  judgment  must  be  acquired  by  the 
student  in  order  to  know  just  when  fifths  and  octaves  may 
be  made  between  the  subject  and  a  note  of  the  counter- 
point. The  following  groups  of  notes  will  be  likely  to 
occur  quite  often  in  his  first  attempts  at  this  order  of 
counterpoint : 


96 


Tonal  Counterpoint 


These  progressions  are  all  bad.  For,  since  the  first  note  of 
each  contrapuntal  group  has  a  harmonic  significance  in 
connection  with  the  subject,  it  is  obvious  that  consecutive 
fifths  and  octaves  are  outlined.  A  somewhat  bad  effect  is 
produced  between  notes  other  than  the  first  of  successive 
groups,  provided  the  fifths  or  octaves  occupy  correspond- 
ing places  in  the  design.  The  following  groups,  for  exam- 
ple, should  be  used  with  caution: 


A  good  general  rule  is  that  this  effect  of  fifths  and  octaves 
caused  by  notes  of  harmonic  significance  is  neutralized  if 
they  are  separated  by  jour  intervening  notes,  or  even  by 
only  one  or  two,  in  case  there  is  distinct  contrary  motion 
between  the  counterpoint  and  the  subject;  for  example, 


Between  two  passing  notes,  or  between  two  notes  of  which 
the  first  is  harmonic  and  the  second  passing,  fifths  are  per- 
missible if  they  are  separated  by  one,  two  or  three  notes: 


(e)  and  (c)  passing  notes 


(e)  is  a  harmonic  and  (c)  a  passing  note 


When  the  passing  note  comes  first  and  the  harmony  note 
second,  the  same  considerations  apply,  except  in  this  case 
the  harmony  note  must  invariably  be  approached  and 
left  stepwise;  for  example, 


(g)  passing  note 
(a)  harmony  note 


In  this  case  the  skip  to  (c)  makes  the  fifth  prominent 


In  this  order  much  more  liberty  is  practicable  in  regard  to 
the  implication  of  chords  of  the  sixth  and  fourth.  While 
writing  two  notes  to  one,  we  saw  that  the  fifth  of  a  triad 


Two-Part  Counterpoint 


97 


should  seldom  be  used  in  the  bass  immediately  after 
its  root  or  third,  at  any  rate  when  approached  by  a  down- 
ward leap.  For  example,  the  following  passage  is  very 
bad: 


m 
i 

i 

u 

1  Lt 

if 

But  in  a  counterpoint  of  four  notes  to  one  of  the  subject, 
the  fifth  of  a  triad  is  often  available  in  the  bass,  provided 
it  comes  between  other  notes  of  the  same  chord,  and  in 
general  does  not  occupy  a  conspicuous  position  in  the 
group;  for  example, 


1 


ri 


Of  these  examples  (a),  (b)  and  (c)  are  perfectly  good,  be- 
cause the  fifth  is  introduced  as  part  of  an  arpeggio,  and  is 
neither  the  highest  nor  the  last  note  in  the  group.  Ex- 
ample (a),  to  be  sure,  is  rather  weak  as  a  mere  arpeggio, 
and  this  figure  should  not  be  used  often.  Example  (J)  is 
somewhat  unsatisfactory,  as  the  g  being  the  highest  note 
of  the  group,  and  also  occurring  on  the  secondary  accent, 
is  plainly  heard  in  its  relation  of  a  fourth  below  the  sub- 
ject. The  fifth  may  even  be  approached  by  a  downward 
leap,  provided  it  occurs  on  a  weak  part  of  the  group;  for 
example, 


Andante  cantabile 


MOZART.    Quartet  in  C  major 


~*  5jT"        * 


98 


Tonal  Counterpoint 


§6 1.  As  the  student  acquires  facility  in  this  kind  of 
contrapuntal  writing,  and  as  his  judgment  becomes  more 
sure,  he  will  understand  the  import  of  the  general  rule, 
that  many  notes  may  be  used  on  weak  parts  of  a  measure 
and  in  unimportant  parts  of  the  general  design,  which 
might  imply  questionable  harmony,  were  there  fewer  notes 
in  each  group  and  were  the  rate  of  motion  slow,  rather  than 
fairly  rapid.  As  a  practical  application  of  this  truth,  the 
leading  tone  may  often  be  doubled,  provided  the  same 
general  considerations  are  observed  as  those  cited  above 
in  regard  to  the  introduction  of  the  fifth. 


good 


good 


bad 


good 


bad 


e* 


*    - 


In  the  examples  marked  good  the  student  will  readily  see 
that  the  leading  note  occurs  between  other  factors  of  the 
same  chord,  and  is  neither  the  highest  nor  the  lowest  note 
of  the  group;  (c)  and  (e}  are  bad  because  these  conditions 
are  not  fulfilled. 

§62.  It  often  happens  that  the  counterpoint  and  the 
subject  approach  each  other.  In  these  circumstances  the 
following  suggestions  should  be  followed:  It  is  generally 
poor  for  the  passing  note  at  an  interval  of  a  second  from  a 
harmony  note  to  continue  till  it  makes  a  unison;  on  the 
other  hand,  the  effect  is  good  when  the  counterpoint  and 
the  subject  start  with  a  unison  and  then  diverge  by  oblique 
motion.  In  this  case  the  unison  should  be  approached 
by  a  leap.  The  following  examples  will  make  the  matter 
clear.  The  same  considerations  apply  to  auxiliary  notes, 
as  an  analvsis  of  the  illustrations  will  show: 


bad 


good 


bad 


§63.  When  the  harmonic  conditions  are  such  that  it  is 
impossible  for  the  counterpoint  to  continue  diatonically, 
it  is  generally  better,  if  a  leap  is  to  be  introduced,  to  have 
it  at  the  former  rather  than  the  latter  part  of  a  measure. 
After  an  accented  note  a  leap  is  effective.  Also  the  last 


Two-Part  Counterpoint 


99 


two  notes  should  generally  flow    smoothly  along   to  the 
next  accent. 


For  instance,  the  first  two  measures  of  example  (6)  are 
stronger  than  the  grouping  found  in  (a).  This  is  a  recom- 
mendation, however,  rather  than  a  rule,  as  in  the  third 
measure  of  example  (6)  the  counterpoint  is  led  up  to  a 
climax  on  the  third  beat,  and  then  a  leap  of  a  third  is 
made  in  the  opposite  direction.  This  was  done  here  to 
avoid  a  repetition  of  the  same  pattern  as  in  the  preced- 
ing measure.  Let  the  student  explain  to  himself  the  use 
of  the  c,  the  first  note  of  the  counterpoint  of  the  fourth 
measure. 

§64.  Attention  is  called  to  the  fact  that  chromatic 
passing  and  auxiliary  notes  above  a  harmony  note  invari- 
ably imply  a  modulation,  whereas  below,  no  change  of 
tonality  is  felt;  for  example, 


I*  I  I  JlJl    J 


in  F         in  C 


in  G 


An  auxiliary  note  below  is  almost  always  at  a  distance  of  a 
semitone,  especially  when  used  in  the  bass;  for  example, 


§65.   Here  follow  a  few  examples  of  first  measures: 


100 


Tonal  Counterpoint 


^grpjirrQ-cE[rir 


The  student  is  advised  to  play  over  the  above  examples 
and  to  analyze  them  carefully.  A  musical  sentence  well 
started  will  often  go  on  almost  of  itself.  Attention  is 
called  to  the  rest  with  which  counterpoint  of  this  order 
should  generally  begin.  The  note  following  the  rest  must 
be  a  concord. 

§66.  The  best  forms  of  cadence  are  the  following: 


°J 

J 

o 

-»- 

Of  the  above  examples,  (a)  and  (b)  are  less  usual  than  the 
others,  though  perfectly  possible;  the  former  with  the  skip 
of  a  diminished  fifth,  and  the  latter  with  a  changing  note, 
(c)  is  also  a  rather  rare  form.  In  this  case  the  f  in  modern 
music  would  generally  be  sharped,  as  explained  above. 
The  student  will  be  tempted  to  use  the  following  forms  of 
cadence.  He  will  readily  see  upon  analysis  why  they  are 
not  permissible. 


Two- Part  Counterpoint 


101 


A  few  examples  are  now  worked  out  for  practical  guidance. 
If  the  leading  principles  explained  above  have  been  under- 
stood, this  kind  of  counterpoint  will  be  not  only  easier, 
but  far  more  interesting  than  the  others.  At  first  very 
short  subjects  are  taken  and  no  modulation  is  required. 


In  this  exercise  first  notice  the  simple,  natural  harmonic 
structure.  Then  as  to  the  counterpoint,  see  how  variety 
is  secured  by  making  occasional  skips  between  flowing 
phrases;  also  notice  what  a  large  range  of  the  scale  is 
traversed.*  At  (a)  and  (b)  attention  is  called  to  the  use 
of  e  against  c,  and  of  c  against  f  without  any  implication 
of  second  inversions,  as  the  e  and  c  are  obviously  used  as 
passing  notes. 


I  vno  I  IV  V  I  ii  I         viio       I 

A  similar  subject  is  here  given  in  the  bass,  but  shortened 
somewhat,  so  that  the  rhythm  is  different.  Even  in  these 
simple  exercises  the  student  is  urged  to  observe  whether 
they  begin  on  a  strong  or  a  weak  beat,  that  is,  whether,  the 
general  rhythm  of  the  phrase  is  trochaic  (-u )  or  iambic  ( u-). 
This  is  settled,  of  course,  by  the  last  note,  which  in  every 
case  is  supposed  to  coincide  with  an  accented  measure, 

*  Most  instructive  examples  of  a  running  bass  may  be  found  in  Beethoven's 
Andante  in  F,  first  in  the  following  passage,  where  the  counterpoint  is  two  notes 
against  one,  and  later  on  in  the  work,  where  the  same  theme  is  treated  with  more 
animated  rhythm  of  four  notes  against  one. 


102 


Tonal  Counterpoint 


that  is,  the  cadences  are  for  the  present  all  masculine. 
This  exercise  needs  no  especial  comment.  Notice  how 
clearly  the  tonality  is  established  at  the  outset  by  the  use 
of  the  tonic  triad.  The  skips  are  invariably  made  at  the 
first  part  of  each  group.  In  the  fifth  measure  an  arpeggio 
is  used  effectively,  to  carry  the  counterpoint  into  a  higher 
range.  We  now  write  a  counterpoint  both  above  and 
below  a  subject  in  the  minor  mode: 


In  this  exercise  notice  first  the  various  forms  of  the  minor 
scale;  for  example,  in  the  second  measure  c,  b!>,  at>,  the 
descending  melodic  form.  Of  course  wherever  dominant 
harmony  is  outlined,  b  it  must  be  used.  At  (a)  the  skip  of  an 
augmented  fourth  is  effectively  introduced.  At  (6)  notice 
the  minor  seventh  bt>,  even  in  an  ascending  passage  on 
subdominant  harmony  between  the  sixth  degree  and  upper 
tonic.  At  (c)  the  ait  is,  of  course,  a  changing  note,  and  the 
melodic  form  of  the  scale  is  used. 


ft 


At  the  beginning  the  counterpoint  crosses  for  a  moment 
above  the  subject.  The  bass  was  started  high  in  this 
way  to  make  its  range  as  wide  as  possible.  On  two 
stringed  instruments  this  doubling  of  the  c  would  not 
be  objectionable.  In  writing  for  the  pianoforte  the  subject 
and  counterpoint  must  not  be  kept  for  long  so  near 
together,  for  the  same  key  cannot  do  two  different  things 
at  the  same  time,  and  the  iteration  is  unpleasant  and 
destroys  the  individuality  of  the  subject.  On  comparison 
with  the  preceding  exercise  the  student  will  notice  how 
many  passages  which  are  valid  in  a  counterpoint  above  a 
subject  are  equally  good  below.  The  observation  of  this 


Two-Part  Counterpoint 


103 


general  truth  will  prepare  him  for  a  form  of  writing  known 
as  double  counterpoint,  to  be  taken  up  later. 

§67.  Here  follow  subjects,  some  of  which  have  been 
treated  in  Chapter  III,  to  which  the  student  is  to  write 
counterpoint,  with  suitable  transposition  of  key,  both  above 
and  below.  In  this  group  no  modulation  will  be  necessary : 


1. 


2. 


P=l 


^  P  /v      0 

r  i  r  i  r  r 


FH 

^tp 

=\ 

—  i 

We  now  give  for  the  advanced  student  a  few  longer  and 
rather  more  difficult  subjects.  These  are  periodic  in  form 
and  imply  simple  modulations.  Whoever  is  not  at  home 
in  the  principles  of  key  relationship  is  advised  to  consult 
any  textbook  on  harmony.*  Note,  for  instance,  that  the 
keys  in  the  first  degree  of  relationship  to  Eb  major  are 
Bb  major,  Ab  major,  C  minor,  G  minor,  and  F  minor. 
In  these  exercises  the  student  should  constantly  strive  to 
put  into  effect  the  recommendation  given  in  Chapter  III, 
§46;  that  is,  the  counterpoint  must  not  be  a  mere  amplifi- 
cation of  a  harmonic  background,  but  must  have  dis- 
tinctive features  of  its  own.  Now  that  the  writing  is  for 
strings,  a  much  freer  use  may  be  made  of  chromatic  passing 
notes  (accented  and  unaccented),  and  likewise  dissonant 
intervals  may  be  introduced  whenever  the  melodic  interest 
of  the  counterpoint  seems  to  wane.  The  following  exer- 
cise is  an  example  of  the  style  which  should  gradually  be 
cultivated. 


*  An  admirable  explanation  may  be  found  in  Prout's  Harmony,  Chapter  X. 


IO4 


Tonal  Counterpoint 


i  i      i       1  1 

EE1  —  ^ 

•a  —  ^ 

j— 

=3^ 

9 

fc= 

la 

S 

1  Jjj 

— 

UjJ 

s 

rJ4 

J  II     i 

CJ                • 

>k    o 

D 

-*»  

b 

o 

ife 


2. 


^ 


(No.  2  transposed  into  E?  major  and  with  the  counterpoint  above) 


*  The  student,  in  fact,  should  soon  be  in  a  position  to  take  a  broad  view  of  contra- 
puntal style  and  of  the  means  whereby  variety  in  harmony  and  in  rhythm  is 
attained.  No  fixed  and  universally  binding  rules  can  be  given,  whereby  one  may 
learn  to  write  good  counterpoint.  A  contrapuntal  voice  may  show  unbounded 
freedom  provided  that  it  is  not  so  incoherent  as  to  lose  all  harmonic  connection 
with  the  other  voices. 


Two-Part  Counterpoint  105 

Duet  for  solo  'cello  and  accompanying  violin: 


HAYDN 


In  connection  with  the  work  on  this  exercise  let  the  student 
compare  Haydn's  treatment  of  the  same  melody  in  his 
string  quartet  —  the  so-called  "  Kaiser  Quartet."  Duet  for 
solo  violin  and  'cello  obligate:* 


BEETHOVEN 


§68.  In  regard  to  counterpoint  with  the  rhythm  of 
three  notes  to  one,  or  six  notes  to  one,  little  additional  need 
be  said.  These  rhythms  are  less  frequently  employed, 
and,  on  the  whole,  are  less  useful  than  that  of  four  notes 
to  one.  In  counterpoint  of  three  notes  to  one,  only  one 
harmony  should  be  outlined  in  connection  with  any  note 
of  the  subject;  an  arpeggio  of  a  chord  is  often  necessary, 
and  the  effect  is  less  weak  than  with  four  notes  to  one. 
As  there  are  always  two  intermediate  notes  between  suc- 

*  Now  that  the  student  has  begun  to  write  simple  pieces  for  strings,  the  teacher 
should  carefully  explain  the  range  and  the  chief  characteristics  of  the  violin,  the 
viola  and  the  'cello.  An  effort  should  be  made  to  bring  musicians  into  the  class 
room  and  to  have  the  exercises  actually  performed,  —  both  the  original  and  the 
corrected  versions.  Nothing  will  cultivate  more  steadily  the  musical  instinct  of 
the  student  than  frequent  opportunities  to  hear  his  work  played.  This  has  been 
done  for  several  years  at  Harvard  University  with  the  most  beneficial  results. 


io6 


Tonal  Counterpoint 


cessive  accents,  it  is  clear  that  two  consecutive  passing 
notes  or  changing  notes  may  often  be  employed;  for 
example, 


i 


r-  f-  r 


A  few  illustrative  examples  are  cited;  they  should  be 
carefully  analyzed  and  other  analogous  passages  looked 
up  from  standard  compositions. 


BEETHOVEN.    Sonata.    Op.  31,  No.  i,  Rondo 


T   r 

BEETHOVEN.     Sonata.    Op.  53,  Rondo 


§69.  Almost  any  of  the  subjects  given  in  the  preceding 
chapters  may  be  treated  with  counterpoint  of  three  notes 
to  one,  and  the  student  should  work  out  a  few.  The 
melody  given  on  p.  84  is  begun  to  show  the  general  style. 


§70.  In    counterpoint    of    six    notes    to    one    it    often 
happens  that  groups  of  the  same  notes  may  be  so  used 


Two-Part  Counterpoint 


107 


with  reference  to  the  primary  and  secondary  accents  that 
the  effect  is  perfectly  good;  for  example, 


- 


r 


whereas  if  the  rhythm  were  that  of  three  beats  to  a  meas- 
ure, and  the  same  notes  were  grouped  as  follows, 


r      r- 

the  effect  would  be  very  weak  on  account  of  the  repetition 
of  the  same  design. 

§71.  We  cite  a  very  instructive  example  of  counter- 
point of  six  notes  to  one  from  the  finale  of  Rheinberger's 
Pastoral  Sonata  for  organ. 


io8 


Tonal  Counterpoint 


§72.  An  exercise  is  now  worked  out  as  a  model  to  the 
student,  who  should  work  out  several  exercises  in  this 
style,  using  some  of  the  short  melodies  already  given  (with 
suitable  alterations  of  the  time). 


§73.  For  this  version  observe  how  often  an  accented 
passing  note  or  a  changing  note  is  used  on  the  fourth  beat 
of  the  counterpoint  (that  is,  on  the  secondary ^  accent). 
The  dissonance  gives  vigor  and  piquancy  to  the  counter- 
point, which  in  this  style  is  often  likely  to  become  tame. 

§74.  Counterpoint  of  eight  notes  to  one  is  compara- 
tively rare,  and  no  practice  is  needed  in  it  save  that  of 
looking  up  and  analyzing  examples.  In  Beethoven's 
beautiful  Rondo  in  G  Major  for  Pianoforte  (Op.  51,  No. 2), 
there  may  be  found  some  very  instructive  passages,  both 
in  six  and  eight  notes  to  one. 


CHAPTER    V 
Syncopated  Counterpoint  —  Rhythmic  Embellishments 

§75.  In  preparation  for  florid  counterpoint,  that  is, 
that  form  of  writing  wherein  the  rhythm  is  varied  with  great 
freedom,  the  student  must  learn  something  of  the  prin- 
ciple of  syncopation.  This  is  a  device  by  which  the  normal 
position  of  the  accent  (on  the  first  of  the  measure)  is 
temporarily  reversed;  the  effect  is  produced  by  tying 
the  accented  half  of  a  measure  to  the  unaccented  half  of 
the  preceding  one.  The  syncopation  may  form  either  a 
consonance  or  a  dissonance  in  connection  with  the  chief 
melody.  The  latter,  in  fact,  is  preferable  where  it  can 
be  brought  about  naturally,  for  then  in  addition  to  the 
variety  of  rhythm  we  secure  temporary  effects  of  dis- 
sonance which  impart  progressive  interest  to  the  music. 
When  the  syncopation  is  a  dissonance  the  student  will 
remember  that  the  harmonic  effect  is  called  Suspension, 
and  we  shall  soon  see  which  are  the  most  useful  suspen- 
sions in  simple  counterpoint.  It  is  possible  to  syncopate 
any  note  of  a  chord,  provided  it  is  either  a  note  common 
to  the  following  chord  or  available  as  the  preparation  of 
a  suspension.  The  most  usual  factors  to  suspend  in  tri- 
ads are  the  third  (4-3)  and  the  root  (9-8)  (in  each  case 
from  the  note  above) ;  though  rarely  a  suspended  fifth 
(6-5)  in  the  midst  of  other  genuine  suspensions  may  have 
the  same  effect.  The  root  of  the  tonic  triad,  however, 
is  often  suspended  from  the  note  below  (7,  8)  —  that  is, 
from  the  leading  tone ;  and  sometimes  the  third  is  suspended 
from  the  second  (2,  3).  All  these  suspensions,  with  the 
exception  of  the  last  (2,  3),  are  equally  available  with 
either  the  root  or  the  third  in  the  bass,  as  will  be  seen  from 
the  following  charts. 


no 


Tonal  Counterpoint 


At  (a)  and  (6)  we  have  a  root  and -a  third  suspended 
from  above.  At  (c)  is  the  rather  ambiguous  suspension 
of  the  fifth.  This,  however,  is  quite  satisfactory  when 
the  bass  outlines  a  first  inversion.  The  a  can  no  longer 
be  a  part  of  the  harmony,  for  a  chord  of  the  sixth  and 
fourth  in  this  connection  would  be  impossible.  At  (d) 
we  have  the  root  suspended  from  below,  and  at  (<?)  the 
third  treated  in  the  same  way.  Let  the  student  ask  him- 
self why  this  effect  would  not  be  possible  in  the  first 
inversion.  The  suspension  of  the  root  and  of  the  third  is 
possible  also  in  the  bass;  the  suspension  of  the  fifth,  how- 
ever, is  ineffective,  as  there  is  no  dissonance. 


J 


ffrS=* 


r—  r 


The  weak  effect  produced  at  (c)  will  be  felt  at  once.  A 
few  short  examples  are  analyzed  in  exemplification  of  the 
preceding  principles. 


.0  ^ 

* 

* 

.-- 

a> 

I' 

^1 

•s» 

^ 

^4= 

•». 

• 

= 

>  — 

I-P- 

•>    1 

_                                  y 

x^  •* 

fcr 

^ 

F 

^.—  • 

^*i 

^  1  

^ 

FjF 

The  student  will  readily  see  that  at  the  places  marked  (*) 
there  are  real  suspensions;  even  the  perfect  fifth  at  (y) 
retarding  the  sixth  gives  the  effect  of  a  suspension.  All 
the  other  tied-over  notes  are  merely  syncopations.  The 
truth  of  the  following  statements  will  now  be  understood: 
First,  that  every  suspension  must  imply  also  a  syncopation, 
though  every  syncopation  need  not  involve  a  suspension. 
Second,  if  the  effect  is  one  merely  of  syncopation,  it  may 
be  resolved  by  either  disjunct  or  conjunct  motion  —  gen- 
erally the  former :  —  whereas  a  real  suspension  must  be 
resolved  stepunse  downwards  or  upwards.  Even  this  last 


Syncopated  Counterpoint 


in 


statement  will  be  modified  when  we  come  to  speak  of 
the  ornamental  resolution  of  suspensions.  The  same  sub- 
ject is  now  treated  with  the  counterpoint  below. 


F%=^ 

*F 

~^n 

Efe 

X 

-N           ^ 

-^            /- 

—  N 

4^ 

—  L— 

=*= 

4= 

•^, 

^ 

vr  I 

T^ 

b 

"X      /• 

;v 

c 

3  —  i  —  1 

—  L-  J 

4=1 

—  f— 

The  syncopation  is  broken  at  (a),  (b)  and  (c).  This  is 
sometimes  advisable  on  account  of  the  range  of  the  melody, 
and  also  to  secure  as  many  real  suspensions  as  possible. 
It  is  often  necessary  at  the  cadence  when  the  counterpoint 
is  in  the  lower  voice.  The  counterpoint  at  (a)  might 
have  been  arranged  as  follows : 


fjj.i'a  *v 
i"*!0  ** 

* 

=F=P 

|;t-r  r 

L^ 

LjiJJ 

g    I 

«^ 

but  the  weak  effect  at  (*)  will  be  readily  noticed. 

§76.  Example  (a)  brings  up  the  question  of  how  far 
the  effect  of  consecutive  fifths  and  octaves  is  neutralized 
by  syncopation.  At  first  sight  it  looks  as  if  there  were 
consecutive  fifths  between  the  first  notes  of  the  third, 
fourth  and  fifth  measures.  But  as  the  harmony  is  out- 
lined by  the  subject  and  the  second  note  of  the  counter- 
point in  each  measure,  the  fifths  are  only  apparent  and 
have  no  harmonic  import  whatsoever.  The  perfectly  clear 
harmony  of  the  passage  will  be  seen  if  we  suppress  the 
syncopation. 


etc. 


4 

-Hro  1  —     —  i  —    —  i  —    —  i  —    —  i  —     —  i  —    1  n 

I 

*) 
P 

>(>a  t, 

6 

6 

6 

6 

iff 

112 


Tonal  Counterpoint 


§77.  The  student  must  constantly  bear  in  mind,  how- 
ever, that  syncopations  do  not  justify  ungrammatical 
harmonic  progressions. 


(ft  -j  -  >( 

in 

Ejg 

t±=pz 

8 

7* 

n 

*>- 

/8" 

7 

5 

/^ 

If  the  above  passage,  for  instance,  be  reduced  to  its  simple 
harmonic  foundation,  by  the  omission  of  the  syncopa- 
tions, it  is  evident  that  we  have  three  consecutive  octaves 
followed  by  three  fifths.* 

§78.  As  in  the  former  varieties  of  counterpoint,  more 
than  three  consecutive  thirds  or  sixths  should  usually  be 
avoided.  When  a  subject  moving  by  steps  would  natu- 
rally call  for  a  harmonization  by  chords  of  the  sixth,  it  is 
better  to  break  the  syncopation  for  a  measure.  Exam- 
ple (6)  is  far  preferable  to  (a). 


monotonous 


better 


JrihIJrJ 


§79.  In  regard  to  fifths  and  octaves  not  separated  by  a 
foreign  chord,  an  infallible  test  of  correctness  is  to  elimi- 
nate the  syncopations.  For  example,  the  following  phrase, 

*  Cases  often  arise  in  which  a  practised  judgment  is  necessary.  In  the  follow- 
ing phrase,  however,  it  is  better  in  general  to  avoid  the  effect  of  consecutive  fifths, 
which  are  merely  delayed  by  the  sixths: 


Although  in  Haydn's  Symphony  in  D  Major  we  find  the  following: 


rrr 


i^ 


Syncopated  Counterpoint 


perfectly  good  as  it  stands,  is  so  no  longer  if  the  synco- 
pation be  broken: 


for  if  we  suppress  the  syncopations  the  harmonic  basis  of 
example  (a)  is 


good 


questionable 


while  example  (6)  gives 


§80.  The  only  satisfactory  form  of  cadence  in  this 
order  is  the  suspension  of  the  leading  tone  by  the  tonic 
(both  above  and  below);  for  example, 


I 


-e-        -O- 

When  the  subject  is  such  that  the  syncopation  cannot  be 
properly  prepared,  a  cadence  from  the  second  order  must 
be  substituted.  For  instance,  if  the  subject  has  the  fol- 
lowing ending, 


though  syncopation  can  be  used  in  a  counterpoint  abov 
—  for  example, 


when  the  counterpoint  is  below,  some  other  form  is  prefer- 
able; for  in  the  following  arrangement 


H4  Tonal  Counterpoint 

c  and  f  (c  the  fifth  and  f  the  original  root)  imply  a  ques- 
tionable six-four  chord.  The  best  cadence  in  this  case 
will  be 


If  the  subject  move  from  the  sixth  degree  to  the  second, 
a  syncopation  is  possible  both  above  and  below;  for  ex- 
ample, 


^     r^    v~    ~P 

r  r~r  r 


while  if  the  subject  moves  from  the  seventh  degree  to  the 
second  a  syncopation  either  above  or  below  is  impossible: 


r  r 


Let  the  student  work  out  for  himself  satisfactory  cadences 
to  the  measures  above,  with  counterpoint  both  above  and 
below. 

§81.  Very  few  exercises  will  be  given  to  work  out  in 
this  order,  for  on  account  of  its  restrictions  it  is  not  only 
the  most  difficult  but  the  most  unattractive  of  all  the 
orders.  In  fact,  in  actual  composition,  syncopation  is 
seldom  continued  unbroken  even  for  as  many  measures 
as  in  our  exercises.  In  these,  however,  the  student  is 
expected  to  use  syncopation  wherever  possible  in  order  to 
acquire  proper  facilitv.  But  syncopation  finds  its  real 
value  in  the  next  order  that  we  shall  study,  —  florid  or 
mixed  counterpoint,  where  it  is  of  the  greatest  practical 
assistance  in  securing  variety  of  rhythm.  In  vocal  music 
but  few  syncopations  are  used  at  a  time,  to  offer  contrasts 


Syncopated  Counterpoint 


in  rhythm  between  the  voices,  to  emphasize  some  impor- 
tant word,  or  to  produce  some  striking  harmony.  In 
instrumental  music  syncopation  is  often  useful  for  vary- 
ing a  melody  at  its  second  appearance  and  to  give  anima- 
tion to  the  rhythm : 


HAYDN.     "  Kaiser  Quartet  " 


BACH.    Organ  Fugue  in  C  major 


fe 


m 


m 


V 


efc. 


Good  examples  of  vocal  syncopations  and  .suspensions  may 
be  found  in  the  "  Messiah  "  Choruses,  Nos.  22,  23,  31  and 
52.  The  following  passage  from  an  "  a  capella  "  chorus 
in  Parker's  "  St.  Christopher"  has  a  very  beautiful  effect 
of  syncopation: 


In  the  Rondo  of  Beethoven's  Pianoforte  Sonata,  Op.  13, 
at  the  beginning  of  the  episode  in  A\>  major,  ftiay  be  found 
a  good  instance  of  syncopation  used  freely  to  vary  a  mel- 
ody, also  in  the  Allegretto  of  Op.  27,  No.  2.  The  middle 
portion  of  the  Adagio  of  Schumann's  Second  Symphony 
furnishes  numerous  examples  of  syncopation. 

§  82.  This  is  a  good  occasion  for  urging  the  student,  as 
his  musical  development  progresses,  to  lay  more  and  more 
stress  upon  the  study  of  actual  music.  The  true  place  to 
learn  musical  grammar  and  to  cultivate  an  artistic  style 
is  found  in  the  living  masterpieces  of  the  great  composers. 
The  student  should  gradually  become  more  and  more 
familiar  with  the  standard  compositions  of  Bach,  Bee- 


n6 


Tonal  Counterpoint 


thoven,  Handel,  Haydn  and  Mozart, — especially  those 
which  are  polyphonic  in  style,  that  is,  Bach's  "  Well- 
Tempered  Clavichord,"  the  two  and  three-voice  Inventions, 
his  organ  Preludes  and  Fugues,  and  his  great  works  for 
voices,  the  string  Quartets  of  Haydn,  Mozart  and  Bee- 
thoven, etc.  He  will  learn  more  real  music  by  carefully 
analyzing  and  committing  to  memory  even  a  few  of  these 
compositions  than  by  reading  any  number  of  theoretical 
treatises.  Let  him  bear  in  mind  that  the  rules  of  harmony 
and  of  counterpoint  have  been  deduced  from  the  works 
of  the  standard  composers. 


EXERCISES 

A   syncopated   counterpoint   to   be   written   above   and 
below  each  subject. 


AT.  B.  —  Here  a  modulation  into  the  dominant  may  be  made  effective. 
4.     Transpose  into  G  major  a  twelfth  above,  and  write  counterpoint  below. 


5. 


6.    Transpose  into  F  minor  an  eleventh  above  for  counterpoint  below. 

§83.  Syncopations  in  counterpoint  of  three  notes  to  one 
are  much  easier  to  handle,  especially  when  the  subject  is 
in  the  bass.  In  this  rhythm  of  three  notes  to  a  measure, 
it  is  often  advantageous  to  use  an  ornamental  resolution 
for  a  suspension.  By  "  ornamental  resolution  "  is  meant 
the  writing  of  a  note  between  the  suspension  and  its  normal 
resolution.  This  interpolated  note  is  usually  a  note  of 
the  chord  over  which  the  suspension  takes  place;  but  a 
changing  note  foreign  to  the  harmony  may  often  be 


Syncopated  Counterpoint 


117 


introduced  with  good  melodic  effect;  for  example,  at  (a) 
we  have  a  suspension  with  normal  resolution: 


£& 


i^.ii> 


fe 


Itf 


at  (6)  an  interpolated  note  which  is  a  factor  (the  fifth)  of 
the  harmony  delayed  by  the  suspension;  and  at  (c}  a 
changing  note,  used  in  the  normal  way,  —  that  is,  it  is  taken 
by  a  leap  of  a  third  and  resolves  diatonically  to  a  note 
within.  To  secure  an  effective  cadence  in  this  order, 
it  is  always  necessary  to  adopt  an  ornamental  resolution 
for  the  sxispension;  for  example, 


J 

J 


r 


At  (a)  and  (c)  the  interpolated  note  is  part  of  the  harmony  ; 
at  (b)  and  (d)  it  is  obviously  a  changing  note.  The  fifth 
of  a  chord  may  even  be  taken  below  the  root  as  an  orna- 
mental resolution,  without  any  ungrammatical  implica- 
tion of  six-four  harmony;  for  example, 


§84.    Two   simple  examples   are  now  submitted  to   be 
analyzed  by  the  student: 


1 


IV 


Ji8 


Tonal  Counterpoint 


Observe  that  in  the  fifth  measure  at  (a)  dominant  seventh 
harmony  is  effectively  used. 


Si 


This  example  is  noteworthy  for  the  variety  in  the  minor 
scale.  At  (a)  we  see  the  melodic  form,  and  at  (b)  the  minor 
sixth  introduced  in  a  descending  passage. 

§  85.   Place  a  syncopated  counterpoint  both  above  and 
below  the  following  subject: 


Although  the  exercises  assigned  to  this  chapter  are  few 
and  simple,  they  should  be  carefully  worked  out.  The 
advantage  gained  will  be  evident  when  we  come  to  the 
next  order,  —  florid  counterpoint. 


CHAPTER    VI 
Two-Part  Counterpoint  in  the  Florid  Style 

§  86.  In  this  order  known  as  "  florid  counterpoint,"  all 
the  forms  heretofore  studied  are  used,  with  the  exception 
of  the  first  (note  against  note),  and  the  object  is  to  secure 
as  far  as  possible  variety  of  rhythm  and  of  melodic 
design.  In  fact,  we  have  here  the  first  opportunity  to  cul- 
tivate and  develop  a  rhythmical  instinct.  Previously  the 
same  rhythm  has  been  followed  throughout  an  exercise, 
but  now  in  general  no  two  successive  measures  should  have 
the  same  rhythm  or  a  like  melodic  outline.  In  his  first 
attempts  the  student  will  doubtless  find  himself  writing 
some  very  unrhythmical  phrases.  A  good  way  to  begin  is 
to  take  the  time  signature  f  and  to  see  how  many  patterns 
may  be  constructed  in  accordance  with  the  fundamental 
principles  of  rhythm.  Some  of  these  principles  briefly 
stated  are  as  follows:  The  accent  comes  on  the  first  and 
third  beats;  therefore  long  notes  should  be  used  on  these 
beats  and  motion  kept  up  on  the  weak  unaccented  beats, 
the  second  and  fourth.  If  several  measures  are  to  consist 
of  intermingled  half  notes  and  quarter  notes,  the  half  notes 
should  occur  in  the  first  part  of  the  measure,  and  not 
vice  versa;  for  example,  the  following  passage  is  very 
bad*on  account  of  the  position  of  the  half  notes  at  the 
end  of  each  group, 


just  where  a  lively  rhythm  should  carry  the  mind  along 
to  the  next  accent. 

RHYTHMIC  PATTERNS 


*  rnr  r  r  i 


t  r  r  u  i  r 


120 


Tonal  Counterpoint 

ba-l  bad 


I  ><  >d  in  two-part  writing.  bad 


very  bad 


In  the  application  of  these  patterns  to  actual  notes  the 
following  observations  may  be  made:  when  the  second 
order  (of  two  notes  to  one)  is  used,  which  is  comparatively 
seldom,  the  second  note  is  tied  to  the  first  beat  of  the  fol- 
lowing measure ;  for  example, 


The  third  and  fourth  orders  are  those  most  frequently 
used  in  florid  counterpoint,  the  former  to  secure  a  lively 
rhythm,  and  the  latter  for  a  temporary  change  of  accent, 
with,  as  a  result,  greater  variety.  There  should  not  be 
too  many  measures,  especially  in  succession,  consisting 
merely  of  four  quarter  notes.  It  is  generally  better  to 
substitute  two  eighths  on  either  the  second  or  fourth  beat ; 
sometimes  on  both.  Figures  like  the  following  are 
always  available: 

good,  to  be  used  rarely 


The  student  is  cautioned,  first,  against  the  use  of  eighth 
notes  on  the  strong  beats,  the  first  and  third;  for  example, 


Two-Part  Counterpoint 


121 


such   combinations   as   the   following   always   disturb   the 
rhythm. 

bad  bad 


Second,   against  allowing  a  leap  to   appear  between  the 
two  eighth  notes;  for  example, 


bad 


iit 


bad 


Figures  such  as  these  give  a  restless  effect  to  the  counter- 
point which  is  seldom  desirable. 

§87.  The  employment  of  the  fourth  order  (syncopa- 
tion) in  florid  counterpoint  requires  some  attention,  as 
much  variety  is  gained  by  the  use  of  ornamental  reso- 
lution. 

The  following  table  gives  some  of  the  most  common  and 
useful  syncopations,  and  it  should  be  carefully  analyzed 
and  committed  to  memory  by  the  student. 


At  (a)  we  see  a  syncopated  note  with  simple  resolution; 
and  at  (6),  (c),  (d),  etc.,  various  types  of  ornamental  reso- 
lutions. Care  must  be  taken  not  to  repeat  the  suspended 
note  and  its  resolution  by  the  ornamental  interpolated 
notes  of  the  second  beat;  for  example,  the  following 
resolutions  are  monotonous  and  weak : 


122 


Tonal  Counterpoint 


The  student  must  clearly  understand  that  the  suspension 
always  resolves  on  the  third  beat  of  the  measure.  For 
instance,  the  following  passage, 


though  tempting,  is  not  valid,  for  it  is  obvious  that  the 
suspended  c  really  does  not  resolve  at  all.* 

§88.  Occasionally  a  syncopated  note,  a  minor  seventh 
above  the  bass,  does  not  resolve  till  the  following  measure ; 
for  example, 


In  this  case  if  an  ornamental  resolution  be  adopted,  to 
quicken  the  rhythm,  it  should  be  above;  that  is, 


^1 ^*  <TZ 


§89.  In  general,  a  suspended  note,  especially  if  it 
be  a  quarter,  should  be  taken  by  a  leap;  example  (a) 
is  far  stronger  than  (6),  in  which  the  ascending  diatonic 
passage,  instead  of  leading  to  a  new  accented  note,  is  merely 
checked  in  its  course. 

(a)  (6) 


1 


§90.  In  the  use  of  ornamental  resolutions  fifths  and 
octaves  often  appear,  but  as  they  have  no  harmonic 
import  they  may  be  freely  used;  for  example, 

8 


*  Although  effects  analogous  to  this  can  be  found  in  music,  they  had  better  nut 
be  used  for  the  present. 


Two-Part  Counterpoint 


123 


In  regard  to  groups  of  four  eighth  notes,  though  possible 
on  either  half  of  a  measure,  they  should  be  used  but  very 
seldom.  When  the  group  occurs  on  the  first  half  of  the 
measure,  the  first  eighth  should  invariably  be  tied  to  the 
last  note  of  the  preceding  measure;  for  example, 


Interpolated  measures  like  the  following, 

bad 


give  the  rhythm  a  spasmodic  animation  entirely  foreign 
to  the  best  style  of  florid  counterpoint.  The  following 
table  gives  some  useful  patterns  for  the  opening  measures. 


The  best  types  of  cadences  are  the  following. 


Occasionally  a  free  rhymic  effect  may  be  produced  in  the 
cadence,  as  at  example  (a)  by  the  use  of  a  dotted  quarter 
note  followed  by  an  eighth  anticipating  the  final  harmony. 
Observe  that  if  the  subject  ends  as  at  example  (b)  and  is 
in  the  upper  voice,  syncopation  is  impossible.  Compare 
the  corresponding  case  in  the  fourth  order.  Florid  coun- 
terpoint must  have  vigor,  unity  and  rhymic  variety ;  hence 


124 


Tonal  Counterpoint 


be  truly  melodious.  So  many  different  types  are  afforded 
of  rhymic  and  melodic  outline  that  the  student  has  little 
excuse  for  writing  monotonously.  It  is,  therefore,  rarely 
good  for  consecutive  measures  to  have  the  same  pattern. 
Passages  like  the  following  are  to  be  avoided : 


4 


t)       S-w- 

§91.  The  beginner  is  advised,  however,  not  to  make 
his  counterpoint  too  elaborate  or  too  animated,  and  in 
regard  to  the  important  quality  of  unity,  he  is  strongly 
urged  to  avoid  the  far  too  common  habit  of  writing  his 
exercises  measure  by  measure.  Nothing  is  more  insidi- 
ous than  the  habit  of  writing  a  measure  of  counterpoint, 
and  then  after  closing  tight  the  ears  and  eyes,  of  proceed- 
ing to  the  next.  An  exercise  finished  in  this  manner  will 
have  about  as  much  real  musical  value  as  a  picture  which 
consisted  of  adjoining  stripes  of  various  colors.  On  the 
other  hand,  it  is  wise  to  read  the  whole  subject  through,  to 
play  it  over,  in  case  it  is  not  vividly  grasped  by  the  inner 
hearing,  and  then  to  sketch  a  general  outline.  Jot  down 
phrases  that  immediately  occur  to  the  imagination,  espe- 
cially at  the  beginning  and  end,  and  fill  in  details  after- 
wards. Strive  at  first  to  cultivate  ingenuity  and  facility 
in  writing,  even  at  the  cost  of  slight  mistakes,  rather  than 
to  have  everything  exact  and  labored.  The  rhythm  should, 
in  general,  begin  in  a  dignified  way  and  become  more  and 
more  varied  and  animated  as  the  end  is  approached.  The 
exercises  are  to  be  regarded  as  instrumental  rather  than 
vocal,  and  ir% writing  them  the  student  should  imagine 
how  they  would  sound  if  performed  on  the  pianoforte,  the 
organ  or  by  two  stringed  instruments.  Good  examples 
of  counterpoint  will  greatly  interest  and  encourage  the 
student,  and  for  this  purpose  nothing  can  surpass  the 
works  of  Bach.  We  recommend  for  analysis  the  first 
dozen  measures  or  so  of  the  following  Fugues  from  the 
"  Well-Tempered  Clavichord":  First  Book,  Fugues  4  and 


Two-Part  Counterpoint 


12 


16;  Second  Book,  Fugues  7,9,  14  and  17.    A  few  examples 
are  now  worked  out  as  models: 


/?/  Violin 


At  (a)  the  sequential  imitation  justifies  the  use  of  the  same 
pattern  in  consecutive  measures.  At  (6)  and  (c)  modu- 
lations are  made  into  related  keys. 

Viola 


Cello 


At  (a)  note  the  effective  use  of  the  melodic  scale  of  C  minor. 

EXERCISES' 


1. 


ft  b  a 


2. 


Piano  forfr 

•n 

'      tt     4.   *  J 

126 


Tonal  Counterpoint 


3. 


f^ 

-4-n  

.x—  • 

N  B 

^^ 

ijr>4     H 

i  n  i  n 

i  —  n 

[  J  flj 

^±= 

n 

s 
s 

in 

. 

_^ 

-iH 

9 

*):g..tft>   4  

^ 
—  R  — 

a 

etc.,  like  No.  5  except 
transposed. 

;^tti" 

6. 


If  the  student  has  thoroughly  grasped  the  principles  set 
forth  in  this  chapter,  and  has  carefully  worked  out  the 
above  subjects,  he  will  derive  much  profit  from  the  setting 
of  florid  counterpoint  to  melodies  which  in  themselves  are 
of  free,  varied  rhythm.  In  these  exercises,  contrast  and 
balance  of  rhythm  between  subject  and  counter-melody 
should  be  earnestly  sought  for;  that  is,  when  the  rhythm 
is  lively  in  one  part  there  need  be  less  motion  in  the  other. 
The  following  short  example  will  illustrate  what  is  meant: 


^rfa 


•«J|JJ 


Two-Part  Counterpoint 
EXERCISES 


1. 


rr 


^ 


2.   2E 


From  HANDEI. 


3. 


4.3 


SI 


^ 


WAf.-VEU 


BACH 


CHAPTER    VII 
Three-Part  Counterpoint 

§92.  If  the  student  has  acquired  the  facility  in  writing 
to  be  expected  from  his  study  of  two-part  counterpoint 
in  the  five  fundamental  orders,  the  hardest  part  of  the 
training  is  over  and  he  will  readily  progress  to  counter- 
point of  various  kinds  in  three  and  four  voices.  In  all  the 
exercises  heretofore  worked  out,  we  must  bear  in  mind 
that  no  matter  what  we  may  have  called  the  two  parts 
with  reference  to  vocal  range,  from  a  harmonic  standpoint 
they  have  been  soprano  and  bass,  that  is,  outside  parts. 
So  far  the  basis  of  our  harmony  has  consisted  of  incom- 
plete or  outline  chords,  for  not  even  a  simple  triad  could 
be  fully  represented.  We  have  invariably  tested  its  valid- 
ity, however,  by  imagining  that  the  two  inner  voices 
were  supplied  and  then  seeing  whether  the  harmonic  pro- 
gressions were  'correct.  But  in  three-part  counterpoint, 
the  added  part  must  define  the  chords  which  the  two  parts 
suggested;  and  whereas  in  harmony  an  added  inner  part 
often  consists  largely  of  holding  notes,  which  merely  bind 
the  harmonies  together,  in  contrapuntal  writing,  on  the 
other  hand,  this  added  part  should  be  as  far  as  possible 
melodic  in  character  and  of  independent  interest.  In  three- 
part  counterpoint  in  general  we  can  have  our  chords  in 
their  complete  form,  with  root,  third  and  fifth  present, 
—  for  even  of  a  seventh  chord  one  of  the  best  arrangements 
is  root,  third,  seventh,  with  fifth  omitted. 

§93.  Any  combination  of  voices  is  possible  in  three- 
part  counterpoint,  and  counterpoint  of  whatever  kind  we 
prefer  may  be  in  any  one  of  the  three  voices;  or  the  motion 
may  be  interspersed  among  the  several  voices  in  the  florid 
style.  We  shall  expect  the  student,  however,  to  work  out 
only  those  exercises  from  which  he  "will  derive  the  most 
technical  training,  and  which  have  the  most  direct  bearing 
on  practical  composition.  For  instance,  it  is  very  rare  for 
a  composer  to  write  three-part  counterpoint  in  notes  of 
.equal  length  (note  against  note),  though  Mendelssohn  has 
for  a  special  effect  harmonized  a  choral  in  this  manner  (No.  9 
in  "  St.  Paul  "),  the  soprano  and«alto  being  doubled  on  the 
melody.  (This  reference  should  be  looked  up.)  As  for  three- 
part  counterpoint  with  the  chief  melody  in  the  soprano 


Three-Part  Counterpoint 


I2g 


and  the  counterpoint  in  the  bass,  or  vice  versa,  all  that  is 
necessary  is  to  take  almost  any  of  the  exercises  already 
done,  separate  the  two  outer  parts  so  that  a  middle  voice 
can  be  inserted,  and  we  shall  have  three-part  counter- 
point of  a  certain  kind.  But  when,  the  subject  being  either 
in  the  soprano  or  in  the  bass,  the  student  has  to  write  a 
contrapuntal  middle  voice  (the  second,  third  and  fifth 
orders  are  most  useful), —  or,  better  still,  when  the  inner 
voice  itself  is  the  subject,  and  the  two  outer  voices,  bass  and 
soprano,  have  to  be  invented,  — such  combinations  yield 
him  real  musical  profit.  In  three-part  counterpoint  the 
chief  new  considerations,  over  and  above  what  remains 
in  force  from  our  studies  in  two-part  writing,  are  three  in 
number:  first,  spacing  of  the  voices;  second,  doubling; 
third,  the  character  of  the  inner  voices. 

§94.  First,  the  three  voices  should  be  spaced  as  equi- 
distant as  possible,  since  this  grouping  gives  the  most 
sonorous  effect;  that  is, 


This  is  often  impossible,  however,  on  account  of  melodic 
range;  in  which  case  the  wide  interval  should  be  between 
the  bass  and  the  inner  part,  and  not  between  the  two  upper 
parts,  at  any  rate  for  long;  that  is, 


but  not 


The  important  factor,  the  third,  should  be  placed  in  the 
upper  or  middle  register  and  not  buried  close  by  the  bass; 
for  example, 


7JO 


Tonal  Counterpoint 


§95.  Second,  doubling.  All  three  factors  of  a  chord 
should  be  present,  especially  on  the  strong  beats,  where- 
ever  this  can  be  effected  without  loss  of  melodic  interest, 
which  is  the  chief  thing  to  be  sought.  For  this  reason  it 
is  often  advisable  to  omit  the  fifth,  and  to  have  the  chord 
consist  of  two  roots  and  a  third,  rarely  of  two  thirds  and 
one  root.  More  rarely  still  it  is  necessary  to  omit  the 
root  and  to  have  the  chord  consist  of  thirds  and  fifths; 
this  causes  harmonic  ambiguity.  A  chord  of  the  sixth, 
however,  is  often  used  in  this  arrangement;  for  example, 


9:  n    o 

=£= 

^= 

fX 

^ 
I 

3^ 

In  general,  however,  doubled  major  thirds  should  be 
avoided  (minor  thirds  are  less  prominent) ,  especially  where 
they  are  adjoining  voices  at  the  distance  of  an  octave;  for 
example, 


The  leading  tone  is  to  be  doubled  very  rarely,  and  only 
when  some  particular  melodic  effect  is  gained  thereby.* 
§96.  Third,  in  three-part  counterpoint  the  student  has 
to  pay  especial  attention  to  the  formation  of  a  melodious 
inner  voice.  In  three-part  writing  for  voices  it  is 
extremely  difficult  to  make  an  inner  voice  uniformly  inter- 
esting on  account  of  the  restricted  range.  But  as  the 
exercises  to  this  chapter  will  be  instrumental,  for  strings, 

*  But,  as  a  last  word  on  this  broad  subject,  any  doubling,  even  at  times  that  of 
the  leading  tone,  is  preferable  to  an  unmelodious  part.  The  following  examples 
from  Cherubini  are  instructive.  At  (a)  we  have  every  chord  complete;  at  (b)  we 
have  Cherubini's  corrections,  brought  about  by  free  doubling,  to  obtain  more  flow- 
ing melodies: 


F^N 

b 

(<n  o 

_ 

- 

O 

O 

<~ 

=8= 

O 

—  «  — 

i 

* 

-***• 

Three-Part  Counterpoint 


organ  or  pianoforte,  we  shall  be  freed  in  a  great  measure 
from  our  limitations.  The  range  of  the  instruments  is 
far  wider  than  that  of  voices.  In  writing  for  instruments 
the  parts  do  not  have  to  be  grouped  so  closely  for  mutual 
support  as  in  vocal  compositions;  hence  more  room  for 
melodic  movement.  Lastly,  we  may  avail  ourselves  freely 
of  the  advantages  of  crossing  the  inner  and  upper  parts. 
This  is  especially  effective  in  trios  for  strings,  where  the 
viola  and  the  first  violin  constantly  cross  (vid.  the  following 
examples  from  Dvorak's  Trio  for  strings,  Op.  74) : 


1$  Violin 


as  well  as  upon  the  organ,  where  the  two  manuals  allow 
free  crossing  without  any  inconvenience  to  the  performer 
(vid.  Bach's  six  Trio  Sonatas  for  organ,  with  some  of  which 
the  earnest  student  should  make  himself  familiar);  for 
example, 


ist  Trio  Sonata,     ist  Movement 


In  writing  for  the  pianoforte,  crossing  of  the  voices  is 
obviously  not  so  effective.  At  first  in  three-part  writing 
the  student  had  better  not  try  to  make  the  inner  part  too 
elaborate.  As  we  have  said,  it  is  characteristic  of  inner 
voices  to  be  more  quiet  and  sustained  than  the  more  promi- 
nent outer  voices.  Hence  repeated  notes  may  often  be 
used  in  an  inner  part  although  they  would  be  intolerable 
in  an  outer.  Indeed,  a  quiet  inner  part  is  often  the  very 


I32 


Tonal  Counterpoint 


thing  to  be  sought.  Suppose  the  chief  melody  to  be  in 
the  bass,  and  the  secondary  contrapuntal  part  in  the 
soprano.  In  this  case,  a  too  elaborate  inner  part  detracts 
attention  from  the  balance  of  the  two  other  parts;  it  may 
often  be  quite  subordinate.  In  two-part  counterpoint  it 
is  best  to  avoid  concealed  fifths  and  octaves  altogether, 
save  where  one  part  moves  by  a  semitone.  In  three  parts, 
however,  they  are  less  objectionable,  and  may  often  be 
used,  when  the  parts  can  thereby  be  made  more  melodi- 
ous. The  considerations  stated  in  §39,  Chapter  II,  still 
remain  in  force.  The  best  cadences  for  the  second  order 
in  three  parts  are  the  following  forms : 


S 


pn'ir 

4i 

h 

i 

s 

s 

r 

o 

b^H 

* 

"*** 

1  —  *.  —  1 

(P 

*9 

r^ 

J 

I 

" 

f±= 

' 

s 

o 

S 

o 

-*»- 

A  few  of  the  most  useful  positions  are  now  worked  out  for 
analysis : 


Three-Part  Counterpoint 


f       s 

»  — 

i» 

> 

„ 

<» 

i! 

J 

C.F 

a 

I 

-»>  ,      r    r 

fj     U        L*.  1 

» 

B 

Jvl 

i 

- 

E 

-< 

= 

^  \  *           -^ 

^v 

0 

- 

= 

r\ 

« 

n 

X 

\ 

('NVI 

r^ 

n 

!J       c. 

=f 

f 

f 

•=p 

-  —  — 

7? 

--^ 

$ 
=f 

r 

f 

, 

r 

r 

„ 

, 

i 

5 

At  (a)  in  Nos.  2  and  3  we  employ  two  harmonies  in  the 
measure;  this  device  is  occasionally  useful.  The  stu- 
dent, however,  should  not  resort  to  it  too  frequently.  In 
No.  4  at  (a)  note  the  minor  seventh  between  tonic  and 
submediant  in  both  ascending  and  descending  progression. 
In  this  exercise  let  the  student  ask  himself  why  it  would 
have  been  unmelodic  for  the  last  note  of  the  counterpoint 
to  be  the  third-c. 


EXERCISES 


Counterpoint  in  inner  part 


1. 


?       n    ±it=g 


Counterpoint  to  be  in  soprano 


etc.      No.  i  transposed 


134 


Counterpoint  in  soprano 


i — (9 — ^  i    , , 

I  r  Mf  p 


3. 


Counterpoint  in  inner  part 


4.1 


Work  two  versions;  counterpoint  in  inner  part,  and  also  in  soprano 


i  r  rrf  r'  i  r 


ir 


§97.  The  exercises  in  the  second  order  have  purposely 
been  made  short  and  few,  for  not  only  are  the  third  and 
fifth  orders  in  three  parts  much  easier,  but  they  are  also 
much  more  interesting  and  useful.  If  the  detailed  expla- 
nations, already  given,  of  the  third  order  in  two  parts 
have  been  fully  understood,  we  may  begin  at  once  with 
the  rhythm  of  four  notes  against  one  in  three-part  writing. 


EXAMPLES  FOR  ANALYSIS 


*T          v> 

C  P. 

" 

. 

ffp 

- 

, 

u 

0 

^ 

^^ 


^ 


Three- Part  Counterpoint 


135 


At  (a)  in  No.  2  is  an  example  of  a  repeated  note  in  an  inner 
part,  and  at  (6)  a  passing  modulation  to  the  dominant  is 
introduced. 


3. 


C.P 

a 

. 

Yd* 

Pftf 

r 

rfrf 

1 

—  FT- 

In  regard  to  No.  3,  note  that,  though  in  general  a  counter- 
point of  four  notes  to  one  should  be  flowing  and  cantabile 
in  character,  at  times  skips  are  necessary  for  harmonic 
reasons  as  at  (a) ;  also  that  they  secure  a  wider  range  and 
often  give  a  vigor  and  life  to  a  passage,  as  at  (6),  which 
otherwise  would  be  rather  monotonous.  The  same  sub- 
ject is  now  treated  in  the  inner  voice;  a  few  chromatics 
have  been  introduced  in  the  counterpoint  to  show  the 
] tossibilities  of  free  treatment: 


4.   C.P 


136 

eS 

C,P. 

''4  >    ' 

Tonal 

9    f    P 

Com 

// 

er 

point 

P 

M 

• 

If 

=1=J 

t=±=|= 

^^F 

6 

.0  ij 

_  « 

1 

| 

± 

'    iii 

=f£ 

N= 

3 

=3^ 

^^ 

§ 

Note  that  tne  exercise  is  begun  with  a  chord  of  the  sixth 
from  the  tonic.  This  may  be  done  occasionally  for  the 
sake  of  variety,  and  in  free  music  it  is  not  uncommon  to 
begin  with  the  first  inversion  of  the  dominant.  At  (a) 
the  tied  note  is  effectively  introduced  by  a  leap.  At  (6) 
it  is  unfortunate  that  the  final  tonic  had  to  be  anticipated, 
but  the  harmonic  demands  of  the  subject  seemed  to  leave 
no  other  way.  The  next  two  examples  illustrate  what 
effective  use  may  be  made  of  groups  of  changing  notes. 


c  P 


Three-Part  Counterpoint 


137 


§98.  When  the  counterpoint  is  to  be  in  the  bass,  the 
student  should  strive  earnestly  to  acquire  the  power  of 
making  this  part  flowing,  characteristic  and  truly  melodi- 
ous. All  aimless  wandering  about  over  a  few  notes  is  in- 
tolerable in  the  bass.  A  beautiful  example  of  a  running 
bass  in  free  pianoforte  style  may  be  found  in  the  Trio  to 
the  Menuetto  of  Beethoven's  Pianoforte  Sonata,  Op.  22. 
The  student  should  search  out  other  examples  for  himself. 
Two  examples  follow  to  show  the  general  style. 


8 


«)   - 

<).    4 

h 

*p 

6 

fr** 

*f 

ffff 

frT 

_«yj 

•V 

TT 

* 

TO 

At  (a)  note  the  effective  progression  of  the  leading  tone 
upward  to  the  third  to  avoid  too  much  of  the  tonic,  espe- 
cially just  before  the  end.  At  (6)  the  two  harmonies  in 
the  measure  prevent  IV  and  V  from  being  adjoining  triads 
both  in  fundamental  position. 

The  same  subject  treated  in  freer  style: 


9. 


^ 


K^^ti  T  .^ 
fD  H  4  *> 


Observe  the  smooth  diatonic  ascent  in  the  soprano,  and 
the  range  and  varied  design  of  the  flowing  bass. 


Tonal  Counterpoint 


tT 

s 

N=t 

b 

—  —  P-H 

1    I  J  *  *  ' 

1  J  r  rn 

i  j  *  —  ' 

p 

u    .. 

0 

., 

III 

d 

—  i— 

-i-i 

-P 

-I~H 

J-P 

1  H 

r  fr  j  ' 

At  (a)  an  effective  modulation  is  made  to  avoid  a  repeated 
note  in  an  outer  voice.  At  (6)  and  (c)  the  octave  skips 
prevent  the  long  diatonic  passages  from  becoming 
monotonous.  At  (d)  the  chromatic  auxiliary  note  gives 
variety  to  the  cadence. 

§99.  At  first  there  is  always  difficulty  in  working  in  the 
minor  mode.  A  few  extra  examples  are  therefore  given 
for  analysis.  It  is  by  no  means  enough  merely  to  read 
these  exercises  through;  they  must  be  played  over  fre- 
quently and  transposed  into  other  keys,  if  the  harmonic 
progressions  and  the  melodic  designs  which  they  illustrate 
are  to  become  a  living  part  of  the  student's  equipment. 


At  (a)  we  see  the  leading  tone  doubled  (a  passing  modu- 
lation into  the  relative  major  is  understood)  to  preserve 
the  diatonic  course  of  the  counterpoint.  At  the  same 
time  there  is  vigorous  contrary  motion  between  the  voices. 


Three-Part   Counterpoint 


At  (a)  we  see  the  inner  part  drop  below  the  bass,  merely 
for  a  moment  and  on  a  weak  part  of  the  group. 


i.  a  i  j  d  i  ,g=F 


,1  J  I  J  ,J 


rif  ri('nr»nrcrrri[' 


i! 


4. 


5. 


{^ 


Tii  r  IT 


Though  the  subjects  given  are  few,  many  exercises  may 
be  worked  out  with  them  by  making  use  of  the  various 
combinations  already  explained,  and  by  suitable  trans- 
position of  key.  All  this  manipulation  is  purposely  left 
to  the  student  under  the  supervision  of  his  teacher.  Only 
by  working  out  his  own  salvation  will  he  acquire  facility 


140 


Tonal  Counterpoint 


in  writing  and  certainty  of  musical  judgment.  Modula- 
tions may  be  freely  introduced,  not  only  where  distinctly 
implied  by  accidentals  in  the  subject,  but  wherever  they 
seem  desirable. 

§100.  We  now  pass  on  to  that  form  of  three-part  writing 
in  which  the  second  and  third  orders  are  combined  in  the 
voices  which  accompany  the  subject,  and  lastly,  we  shall 
have  one  or  both  these  voices  in  the  florid  style,  while  the 
subject  may  be  of  notes  uniform  in  length,  or  sometimes 
itself  a  melody  of  varied  rhythm.  By  that  time  the  stu- 
dent's writing  will  be  entirely  free,  and  his  object,  to  make 
all  the  voices  equally  melodious  and  free  in  rhythm. 


¥A— 

f= 

jrf 

fffp 

P 

Ssi 

£ 

3BS 

~+K. 

*P 

IL_I  — 

wi>*  dl  |  1    FJ-" 

PC 

4-(-^ 

3^ 

This  example,  combining  two  varieties  of  rhythm,  requires 
no  explanation.  In  counterpoint  of  this  kind  certain  very 
useful  effects  of  dissonance  may  be  produced  between  the 
accompanying  voices,  by  the  use  of  accented  passing  notes 
and  of  changing  notes,  provided  that  the  voices  are  in 
contrary  motion,  and  that  each,  or  at  any  rate  the  part  in 
quarter  notes,  progresses  diatonically.  By  these  devices 
the  counterpoint  secures  more  freedom  and  individuality, 
and  the  incidental  dissonances  serve  to  prevent  the  har- 
monic background  from  becoming  commonplace.  A 
group  of  illustrative  examples  is  given,  which  will  repay 
careful  analysis.  It  is  not  enough  that  these  illustrations 
and  subsequent  ones  should  be  merely  read;  they  must 
be  played  over  often,  and  even  transposed  into  other  keys. 

I     . *c. 


P 


Three-Part  Counterpoint 


141 


Here  at  (a),  (&)  and  (c)  we  have  dissonant  effects  between 
the  two  upper  voices  produced  by  the  use  of  accented  pass- 
ing notes.  Note  that  between  either  one  of  the  two  upper 
voices  and  the  bass,  the  harmonic  relationship  is  in  accord- 
ance with  the  usual  rules. 

ft  utt 


Here  the  effective  scale  passage  would  justify  almost  any 
passing  dissonance  if  the  harmonic  foundation  were  sound. 
Occasionally  a  dissonant  passing  note,  following  the  anal- 
ogy of  "  changing  notes,"  may  leap  a  third  in  the  opposite 
direction  from  its  normal  course.  Combinations  of  inde- 
pendent voices  like  the  following  are  very  characteristic, 
although  they  are  not  to  be  used  too  often: 


At  (a)  and  (6)  we  see  leaps  of  a  third  in  the  counterpoint, 
after  a  temporary  dissonant  seventh  has  been  formed. 


a^ 

4»  /: 


* 


*6 


^ 


S 


^^ 


At  examples  (a)  and  (6)  we  find  contrary  motion  between 
the  parts  making  the  temporary  dissonance.  This  is 
usually  advisable,  but  at  (c)  we  see  a  corresponding  effect 


142 


Tonal  Counterpoint 


with  parallel  motion.  The  combination  is  justified  by  the 
fact  that  both  voices  descend,  and  that  the  second  harmony 
in  the  measure  is  a  chord  of  the  sixth. 


In  this  example  the  two  adjacent  sevenths  are  of  good 
effect,  as  the  c  is  accounted  for  as  an  auxiliary  note,  and 
the  b  as  an  accented  passing  note.  The  student  will  read- 
ily see  that  the  harmony  outlined  is  a  chord  of  the  second 
between  two  chords  of  the  sixth.  In  the  following  meas- 
ure from  Bach's  first  Trio  Sonata  for  Organ  is  a  good  illus- 
tration of  freedom  in  the  use  of  dissonant  passing  notes : 


I       J 


The  student  will  find  many  analogous  passages  in  the  same 
sonata.  We  give  one  last  interesting  example  quoted 
from  Dubois: 


i 


Two  short  exercises  are  given  for  the  student  to  complete :  * 


*  It  is  left  for  the  teacher  to  decide  how  much  practice  the  individual  student 
needs  in  these  strict  combinations. 


Three-Part  Counterpoint 


II  J  4.  j  r  r  r  1  -  -  !  -  ! 

r—i 

§  %  *  \  f=^ 

=^T^ 

[5-4          |I  — 

Pr^ 

B 

! 

4*- 

^ 

>-^  JF  J 

B 

fr*"  Jr  Ji 

_J_ 

L|  — 

§101.  A  few  examples  are  now  submitted  of  three-part 
counterpoint  in  which  one  or  both  of  the  accompanying 
voices  is  in  the  florid  style.  In  this  kind  of  writing  the 
student  must  practise  reserve  in  the  use  of  eighth  notes. 
Seldom  more  than  two  in  a  group  are  to  be  used.  The 
motion  must  not  be  kept  for  long  exclusively  in  one  voice ; 
on  the  other  hand,  we  should  strive  for  contrast  and  bal- 
ance of  rhythm  between  the  contrapuntal  voices.  The 
general  style  will  be  somewhat  as  follows: 


FMl 

—  Hi 

^<^  • 

•*». 

.  -nj. 

/> 

i  —  jj. 

rn 

—f- 

%)  4  g 
3 

- 

( 

T     • 

» 

— 

~ 

£ 

-e- 

s 

Ui 

1 

Of  these  examples  (a)  is  somewhat  better  than  (b)  in  which 
at  (*)  the  inner  voice  lacks  rhythm  for  rather  too  long  a 
time.  Often  a  monotonous  holding  note  may  be  avoided, 
without  any  alteration  in  the  harmony,  by  some  such 
rhythmic  device  as  this: 


tr 


144 


Tonal  Counterpoint 


Note  that  when  two  voices  are  in  florid  style,  dotted  notes 
play  an  important  part  in  securing  variety  of  rhythm. 
When  they  are  introduced,  care  must  be  taken  to  keep  ur 
vigorous  motion  in  the  neighboring  voice.  A  few  short 
subjects  are  now  worked  out  for  analysis.  This  style  of 
writing  will  furnish  the  student  the  most  valuable  practice 
he  has  had  thus  far.  Nothing  will  help  so  much  toward 
his  command  of  free,  flowing  part-writing  as  the  ingenuity 
and  facility  derived  from  the  careful  study  of  these  exer- 
cises : 


r^ 

F 

^ 

^j 

x- 

v 

Ff 

I-H^H 

— 

»- 

_^~ 

•v 

fe^ 

s 

-*%tH 

E= 

^ 

J 

^-^ 

r« 

It  is  well  to  individualize  the  accompanying  voices  by  let- 
ting them  enter  at  different  parts  of  the  first  measure,  or 
even  sometimes,  as  in  the  example  just  given,  at  entirely 
different  measures. 


9 

•N 

s- 

N 

f 

] 

f 

r 

rf-- 

fc 

- 

t 

= 

- 

^\- 

— 

In  the  above  example  note  carefully  the  balance  of  rhythm 
between  the  two  lower  voices. 


5^ 

±K= 

/  — 

\ 

-rrf 

-iftg" 

""HI 

eJ 

^i  

^ 

^i 

P^ 

*  x—  • 

i* 

" 

/ 

•s 

ft 

, 

^ 

*  4*    J 

=  =*= 

T?1^ 

— 

—  y 

Three-Part  Counterpoint 


145 


At  the  beginning  the  octave-leaps  in  the  outer  voices 
answer  each  other  effectively.  Notice  the  flowing,  melo- 
dious character  of  the  bass  part  throughout  its  range. 


At  (a)  is  a  good  example  of  a  passing  dissonance  formed  by 
an  auxiliary  note  in  the  alto  against  a  passing  note  in  the 
bass.  Effects  like  this  prevent  the  counterpoint  from 
becoming  dull  and  uninteresting.  At  (6)  a  group  of  four 
quarter  notes  is  introduced  in  the  latter  part  of  the  meas- 
ure. Such  groups  must  not  be  used  often,  as  they  tend 
to  give  an  undue  restlessness  to  the  rhythm.  The  student 
is  urged  to  pay  particular  attention  to  those  exercises  which 
have  the  subject  in  the  inner  voice,  as  in  them  he  may 
practise  at  the  same  time  the  formation  of  a  good  bass  and 
a  good  melody.  A  short  example  follows. 


* 


At  (a)  we  meet  for  the  first  time  with  a  dotted  quarter 
note.  They  are  useful  occasionally  for  variety  of  rhythm, 
provided  the  motion  is  kept  up  in  another  voice. 


EXERCISES 


To  this  subject  write  two  lower  voices  in  florid  counter- 
point. 


146 


Tonal  Counterpoint 


z.m 


Two  upper  voices  in  florid  counterpoint : 


To  this  choral  melody  in  the  alto  a  bass  and  soprano  are 
to  be  written;  the  rhythm  of  two  quarters  against  each 
half  is  to  be  kept  up  in  one  or  other  of  the  voices.  A 
possible  beginning  would  be  the  following: 


m 

1 

ffi 

^ 

s 

3 

i 

c 

— 

, 

.ztrp 

§102.  The  student  who  has  worked  intelligently  and 
faithfully  at  the  somewhat  formal  and  gymnastic  exer- 
cises of  the  foregoing  chapter  may  now  attempt  some  work 
of  a  more  distinctly  artistic  nature.  Very  useful  and  inter- 
esting practice  is  afforded  by  the  composition  of  short 
trios  for  organ  or  for  strings,  either  with  a  choral  melody 
as  a  basis  or  with  all  three  voices  entirely  original.  Good 
examples  of  this  style  of  writing  for  organ  may  be  found 
in  Merkel,  Op.  39,  and  in  Rheinberger,  Op.  49.  Quite 
pleasing  short  pieces  may  be  composed  with  either  the 
major  or  minor  scale  as  the  chief  melody  in  any  one  of  the 
voices.  Two  examples  follow, —  first,  the  major  scale  as 
subject  in  the  bass: 


Three-Part  Counterpoint 


147 


In  the  above  example  note  how  the  contrapuntal  phrases 
in  the  two  lower  voices  answer  and  balance  each  other. 


Tonal  Counterpoint 


As  the  scale  is  the  chief  melody,  of  course  the  melodic  form 
is  used.  At  (a),  (6)  and  (c}  we  see  the  introduction  of 
chromatic  auxiliary  notes.  At  (d)  the  leading  tone  in 
the  inner  part  descends  in  order  to  gain  a  complete  chord 
on  the  first  beat  of  the  measure.  At  (/)  the  augmented 
second  is  used  in  a  descending  passage  to  give  character 
and  variety.  This  interval  is  easy  of  execution  on  strings 
if  the  tempo  be  not  too  rapid.  The  student  may  now 
write  two  flowing  melodious  voices  above  the  minor  scale 
in  the  bass.  A  good  beginning  would  be  as  follows : 


Several  trios  should  now  be  written,  both  in  major  and 
minor,  in  quadruple  as  well  as  triple  rhythm,  with  the 
scale  as  subject,  in  each  of  the  three  voices  in  turn.  Those 
which  have  the  scale  in  the  inner  voice  afford  particularly 
good  practice.  A  trio  with  the  major  scale  in  the  inner 
voice  might  begin  as  follows: 


3'  *J£Tr  ^ 

vfr. 

ifo    *" 

T  W      1 

rLJ 

These  two  exercises  may  be  extended  at  will  to  the  com- 
pass of  small  pieces  by  means  of  several  measures  of  intro- 
duction in  two  parts,  before  the  scale  melody  enters,  and 
by  the  addition  of  a  free  coda. 

§103.  We  may  now  attempt  some  three-part  counter- 
point in  free  style  for  strings  and  for  the  organ,  using  as 
subjects  chorals  and  various  periodic  melodies.  In  these 
the  bass  part  may  be  treated  with  freedom,  and  not  sounded 
on  eve.ry  beat.  A  judicious  introduction  of  rests  will 
give  lightness  and  variety  to  the  lower  voice.  One  or  two 
exercises  are  begun  as  models  of  style,  and  then  some 


Three-Part  Counterpoint 


149 


melodies  are  given  at  which  the  student  unassisted  ma}' 
try  his  own  hand  : 


In  connection  with  this  exercise  observe  the  effective  use 
to  be  made  of  pizzicato  and  arco  phrases  in  the  'cello  part. 
The  light  bass  makes  the  flowing  inner  part  stand  out  with 
greater  prominence.  Where  the  voices  are  rather  more 
widely  separated  than  would  ordinarily  be  the  case,  as  at 
(a),  it  is  well  to  have  the  bass  sostenuto,  that  is,  coll'  arco,* 
to  give  more  support  to  the  upper  voices. 

§104.  As  three-part  contrapuntal  writing  is  particularly 
effective  upon  the  organ,  we  may  now  begin  a  simple  trio 
for  that  instrument,  using  a  well-known  choral  melody: 

Sw. 


*  Coll'  arco  =  with  the  bow. 


Tonal  Counterpoint 


At  (a)  note  the  chromatically  altered  triad,  from  which 
the  so-called  Neapolitan  sixth  chord  is  derived,  in  the 
fundamental  position.  At  (ft)  is  an  effective  accented  pass- 
ing note. 


EXERCISES 


Here  the  sequence  would  seem  to  justify  the  use  of 
the  same  figure  for  successive  groups  in  the  counter- 
point. 


At  (a)  and  at  (c)  we  have  the  arpeggio  of  the  tonic  and 
dominant  chords.  In  all  writing  for  strings  arpeggi  may 
be  freely  used.  They  serve  not  only  to  define  the  harmony 
clearly,  but  also  to  give  a  more  extended  range  to  the  coun- 
terpoint. At  (ft)  the  octave-skips  are  melodically  charac- 
teristic and  help  to  avoid  the  constant  repetition  of  notes 


Three-Part   Counterpoint 


in  the  same  register.  In  contrapuntal  writing,  —  in  fact, 
to  a  greater  or  less  extent  in  all  melody  formation,  —  the  stu- 
dent should  not  forget  to  look  along  the  whole  range  of 
the  melody,  and  to  avoid  rigorously  all  aimless  wandering 
.back  and  forth  over  a  limited  compass  of  notes.  In  gen- 
eral, the  broader  sweep  a  melody  has,  the  more  character- 
istic and  interesting  it  will  be. 


•  tS?  Violin 


\ 

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—  « 

F 

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— 

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b= 

After  working  out  the  above  exercise  it  will  prove  of  value 
for  the  student  to  compare  its  harmonic  basis  with  that 
of  No.  i.  He  will  see  that  the  melodic  intervals  are  iden- 
tical in  both  exercises,  the  only  changes  being  those  of 
kev  and  rhvthm. 


4. 


1st  Violin 


$  tU*', 

Wota 


'rr'rrC. 


r^  pnp». 


At  (a)  the  inner  voice  is  crossed  above  the  melody.  Hence- 
forth this  effect  may  occasionally  be  introduced  to  broaden 
the  range  of  the  counterpoint.  In  free  writing  for  strings, 


152 


Tonal  Counterpoint 


that  is,  in  the  string  quartets  of  Haydn,  Mozart  and 
Beethoven,  the  two  upper  voices  move  about,  one  above 
the  other,  with  the  greatest  freedom. 


The  student  may  now  try  a  well-known  melody  from 
Beethoven  in  the  inner  voice,  with  a  flowing  counter- 
melody  above  and  a  light  bass : 


6.   l?f  Violin 


f 


n 


, 
PMC. 


§105.  Valuable  practice  in  counterpoint  of  three  notes 
against  one  may  be  secured  by  taking  exercises  Nos.  4 
and  5  and  altering  the  time  so  that  the  melodies  will  stand 
as  follows.  These  exercises  are  difficult,  but  the  student 
is  urged  to  work  at  them  steadily.  They  practically 
exemplify  a  motion  in  triplets  which  is  often  found  very 
useful  in  free  composition  (see,  for  example,  the  Finale 
of  Brahms'  Sonata  in  F  minor  for  pianoforte). 


7 'hrce-Part  Counterpoint 


7. 


«)  ». 


iaggg 


Before  working  out  Exercises  7  and  8,  the  student  should 
carefully  analyze  the  composition  of  the  three-note  groups 
in  the  counterpoint  of  the  opening  measures.  In  gen- 
eral, in  counterpoint  of  three  against  one,  arpeggi  must  be 
freely  used  for  a  part  of  the  group  at  least.  It  is  seldom 
that  a  diatonic  phrase  can  be  continued  for  any  length. 
Often  an  accented  passing  note  will  be  found  useful  for 
the  introduction  of  a  short  run  as  at  (a).  Let  the  stu- 
dent ask  himself  why  the  leading  tone  is  resolved  as  at  (b). 


CHAPTER    VIII 
Four-Part  Writing 

§106.  We  shall  now  begin  writing  in  four  parts;  at  first 
in  very  simple  style  for  voices,  and  later,  in  freer  style  and 
at  greater  length,  for  strings  and  for  organ.  The  fourth 
voice,  though  it  adds  much  to  the  completeness  of  the 
harmony,  increases  but  little,  if  in  any  way,  the  difficulty 
of  the  task.  The  student  who  has  mastered  the  princi- 
ples set  forth  in  the  chapters  on  two-  and  three-part  writ- 
ing will  need  few  preliminary  recommendations  before  he 
works  in  four  parts.  He  must  continually  bear  in  mind, 
however,  that  even  in  the  simplest  note-against-note  writ- 
ing for  voices,  it  is  never  enough  to  have  the  harmony  cor- 
rect and  the  progressions  valid.  The  melodic  interest  of 
each  voice,  individually  and  in  relation  to  the  others,  is 
the  point  for  which  he  must  strive.  To  secure  this  end, 
the  voices  may  sometimes  be  crossed,  especially  the  two 
inner  voices  (even  the  alto  is  now  and  then  taken  above 
the  soprano  for  a  note  or  two,  although  the  bass  is 
very  rarely  crossed  above  the  tenor).  Occasionally  two 
adjoining  voices  may  overlap;  that  is, 


As  to  repeated  notes,  the  harmonic  considerations  regarding 
the  advisability  of  retaining  in  the  same  voice  the  common 
note  of  consecutive  chords  do  not  apply  here,  because 


£H  —  n- 

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6 
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6 

in  contrapuntal  writing  repeated  notes  in  general  make  for 
monotony  rather  than  for  melodic  life  and  interest.  For 
example,  the  combinations  at  (6)  and  (c}  are  better  con- 
trapuntally  than  that  at  (a)  on  account  of  the  freedom 


Four-Part    Writing 


'55 


of  movement  of  each  voice.  Only  at  (c)  is  there  a  repeated 
note  in  the  tenor.  We  must  distinguish  carefully  between 
outer  and  inner  voices.  Repeated  notes  in  the  inner 
voices  are  often  necessary  and  even  effective  in  contrast  to 
the  more  animated  outer  voices.  In  the  soprano,  how- 
ever, there  should  rarely  be  more  than  one  repeated  note, 
and  in  the  bass,  with  very  few  exceptions,  repetition 
should  be  avoided  altogether.  A  stationary  bass  instantly 
destroys  the  melodic  flow  and  life  of  this  most  important 
6ll;ne  parts.  Tne  student  is  cautioned,  nevertheless,  in 
Tus  early  attempts  at  four-part  writing  not  to  try  to  make 
all  the  voices  equally  melodious  at  the  same  time.  Even  if 
this  were  possible,  it  would  be  hardly  desirable,  for  as 
counterpoint  is  essentially  a  matter  of  contrast,  a  parti- 
cularly melodious  voice  is  invariably  felt  to  be  so  in  com- 
parison with  other  less  melodious  adjoining  voices,  or 
possibly  with  those  voices  which  are  melodious  in  some 
different  way;  as,  for  example,  where  a  slow  sostenuto 
melody  in  one  voice  is  contrasted  with  one  of  bolder 
intervals  and  of  more  animated  rhythm  in  another  voice. 
Only  in  the  most  elaborate  "  a  capella  "  works  of  Bach, 
for  instance,  or  in  the  complex  tissue  of  modern  orchestral 
writing  are  all  the  parts  of  equal  melodic  importance  for 
any  length  of  time.  The  student  must  cultivate  the  power 
to  look  along  the  whole  length  of  a  part,  and  must  see  to 
it  that  somewhere  in  its  course  it  shall  arise  and  "  utter 
some  glorious  thing." 

§107.  We  now  give  a  few  illustrations.  Though  the  first 
exercises  are  for  voices,  so  far  as  style  is  concerned,  no  at- 
tempt is  made  as  yet  to  use  actual  words.  Words  of  cor- 
responding metrical  rhythm  can  easily  be  imagined,  how- 
ever, in  connection  with  all  these  vocal  exercises,  and  in 
no  case  should  the  student  fail  to  sing  over  each  one  of 
the  parts.  The  naturalness  of  the  intervals  and  the  mel- 
odic life  of  the  part  are  best  proved  by  actual  singing. 


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Though  these  exercises  at  first  are  to  be  mainly  note 
against  note,  passing  notes  may  be  used  occasionally  for 
the  formation  of  flowing  melodious  phrases  in  the  several 
voices.  Upon  examination  of  each  of  the  three  lower 
voices  in  the  above  exercise,  we  find  first  a  good  though 
simple  bass,  that  is  there  are  no  repeated  notes,  a  very 
ample  range  is  secured,  the  part  is  an  effective  combina- 
tion of  diatonic  phrases  and  natural  leaps,  and  lastly,  the 
part  when  sung  is  felt  to  have  an  onward  sweep  from 
beginning  to  end. 


The  writer  has  actually  known  this  bass  to  be  written  to 
the  above  melody,  and  if  harmonic  correctness  were  the 
only  consideration,  it  would  be  a  perfectly  possible  lower 
part.  But  when  examined  as  a  professed  melodious  outer 
part,  it  is  seen  to  be  decidedly  inferior  throughout  its  course, 
for  it  either  weakly  .repeats  itself  or  leaps  aimlessly  about. 
In  the  two  inner  voices  we  find  as  usual  repeated  notes, 
but  the  alto  from  the  fifth  to  the  tenth  measure  has  a  mel- 
odious phrase,  while  the  tenor  has  an  unusual  amount  of 
range  and  variety.  In  this  case  the  tenor  is  a  better  inner 
voice  than  the  alto.  In  simple  writing  for  voices  we  shall 
seldom  be  able  to  make  the  alto  and  tenor  voices  equally 
good.  We  now  transpose  the  same  subject  into  G  major 
and  place  it  in  the  bass,  with  one  altered  note  at  the  end 
to  secure  a  better  cadence.  Our  aim  must  now  be  to  com- 
pose a  good  counter-melody  in  the  soprano  and  to  make 
the  inner  voices  as  varied  as  the  simple  style  will  allow. 


Four-Part    Writing 


157 


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In  this  setting  also  the  tenor  is  a  rather  more  melodious 
voice  than  the  alto. 

§108.  At  the  discretion  of  the  teacher,  this  melody  and 
the  subsequent  ones  may  now  be  placed  in  the  alto  and 
tenor  voices.  It  is  freely  acknowledged  that  these  exer- 
cises, even  when  in  simple  style,  are  difficult.  Never- 
theless the  good  results  coming  from  an  intelligent  and 
methodical  practice  upon  them  are  so  lasting  and  so  evi- 
dent that  the  student  is  urged  to  persevere.  In  this  sub- 
ject, as  in  others,  there  is  no  short  and  easy  road  to  the 
summit  of  Parnassus.  Nothing  but  the  most  consci- 
entious work  will  ever  equip  a  man  with  the  facile  ingen- 
uity and  the  sure  judgment  which  are  the  most  valued 
characteristics  of  the  cultivated  musician.  We  must  always 
remember,  moreover,  that  there  is  no  glory  in  coun- 
terpoint exercises  per  sc;  they  are  not  an  end  in  them- 
selves, but  a  means  to  an  end,  namely,  —  the  power  of 
free  part-writing.  So  at  this  point  in  his  studies,  con- 
tinuing at  the  same  time  his  strict  practice,  the  student 
may  well  refresh  his  mind  along  various  side  lines.  First, 
he  should  try  his  own  hand  at  original  composition,  that 
is,  short  four-part  songs  and  hymn  tunes,  at  first  in 


I58 


Tonal  Counterpoint 


"  a  capella  "  style,  and  later  with  simple  accompaniment.  If 
the  student  has  any  genuine  aptitude  for  musical  com- 
position, and  if  the  study  of  counterpoint  is  to  mean  any- 
thing more  to  him  than  a  general  mental  training,  he  must 
have  often  felt  the  instinct  to  utter  some  musical  thoughts 
of  his  own.  This  feeling  he  should  from  now  on  sedu- 
lously cultivate.  In  fact,  counterpoint  as  a  living  study 
is  of  little  value  except  as  it  trains  us  to  express  our  own 
thoughts  with  greater  ease  and  certainty.  The  musical 
imagination,  like  anything  else,  grows  stronger  under  reg- 
ular practice.  Secondly,  he  should  analyze  the  most 
noteworthy  chorals  of  Bach,  Mendelssohn  and  others,  with 
reference  both  to  their  harmonic  and  their  contrapuntal 
aspects.  This  work  will  be  found  to  be  most  interesting 
and  stimulating.  Works  which  contain  particularly  beau- 
tiful chorals  are  the  "  Passion  Music  according  to  St. 
Matthew,"  of  Bach;  the  "Christmas  Oratorio"  of  the 
same  composer;  the  "  St.  Paul,"  and  "  Elijah  "  of  Men- 
delssohn, and  Bach's  Cantatas. 


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In   this   exercise   we   have   a   periodic   melody   of    sixteen 
measures,  consisting  of  two  sentences  of  eight  measures 


Four-Part    Writing 


159 


each.  Each  sentence  is  divided  into  two  four-bar  phrases 
which  in  turn  may  be  subdivided  into  sections  of  two 
measures  each.  By  a  still  finer  subdivision  we  reach  the 
motive,  which  in  this  case  is  an  accented  note  preceded 
by  one  unaccented. 

§109.  Henceforth,  before  beginning  the  harmonization 
of  given  melodies,  the  student  should  sing  and  play  through 
the  entire  melody,  and  count  the  number  of  measures. 
Most  melodies  contain  an  even  number,  that  is,  eight, 
twelve,  sixteen,  etc.,  and  these  will  subdivide  naturally 
into  phrases  of  two  or  four  measures  in  length.  Although 
the  student  who  has  been  well  grounded  in  harmony  will  be 
familiar  with  the  usual  types  of  cadence,  authentic,  plagal, 
half  cadence,  deceptive,  etc.,  he  should  now  strive  for 
familiarity  with  all  the  cadential  possibilities  for  the  ends 
of  phrases.  A  phrase  may  finish  on  any  degree  of  the  scale, 
and  this  in  turn  may  be  approached  from  any  degree.  It 
is  very  valuable  practice  to  make  out,  under  the  guidance 
of  the  teacher,  a  table  of  all  the  possible  cadences  for  the 
several  scale  degrees.  For  instance,  a  phrase  ending  on 
the  tonic  will  have  one  of  the  following  progressions : 


A  little  thought  will  show  that  each  of  these  groups  may 
have  several  different  harmonizations  which  in  turn  may 
be  used  according  as  they  occur  in  the  course  of  a  melody 
6r  at  the  end  of  the  last  phrase,  (a)  and  (b)  allow  the  fol- 
lowing different  treatments: 


cfcic 

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Tonal  Counterpoint 


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It  is  obvious  that  the  notes 


| fir  ii  rid 


can  be  found  also  in  C  minor  and  will  allow  an  equally 
varied  harmonization  in  that  key.    (c)  will  give  us  either 


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c 

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or  will  imply  a  modulation  to  the  key  of  A  minor. 


tft 


r 


In  like  manner  the  student  should  make  out  a  chart  for 
phrases  ending  on  the  supertonic,  that  is,  for  the  follow- 
ing groups: 


o  ii     i  o 

r  II  r  i  f 


P          P 

r  II  f  I  r 


and  so  on,  with  all  the  scale  degrees.  Now  to  return  to 
the  melody  in  F  minor  given  on  p.  158,  the  student  will 
see,  on  counting  the  measures,  that  the  chief  cadences 
occur  at  (a),  (6),  (c),  (d),  (e)  and  (/), 


Four-Part    Writing 


s 


although  each  group  of  two  notes  has  a  more  or  less  defi- 
nite cadential  effect.  At  (a)  we  have  used  a  deceptive 
cadence  to  avoid  any  effect  of  finality  at  the  very  outset. 
At  (6),  where  a  diminished  seventh  chord  is  resolved  into 
its  own  tonic,  both  chords  are  in  inverted  positions  in 
order  to  keep  up  the  feeling  of  progress.  At  (c)  we  have 
a  cadence  in  the  dominant  of  the  relative  major,  and  at 
(d)  a  perfect  cadence  in  the  related  key  of  Di>  major  (a 
modulation  being  demanded  by  the  gl>  in  the  melody 
itself).  At  (e)  instead  of  the  cadence  used  there  might 
have  been  a  half  close  in  F  minor;  that  is, 


but  as  the  melody  must  soon  end  in  that  key,  more  variety 
is  obtained  by  holding  off  from  it  as  long  as  possible.  If 
the  student  will  now  play  through  the  above  exercise,  he 
will  observe  that  each  cadence  is  different  from  any  one 
of  the  others.  This  matter  of  variety  of  cadence  is,  one  of 
the  most  important  points  that  have  been  so  far  discussed. 
There  is  hardly  any  more  practical  or  interesting  way  to 
develop  musicianship  than  in  trying  to  obtain  character- 
istic and  varied  cadences.  The  same  cadence  should 
seldom  be  used  twice  in  a  melody,  and  it  is  never  good  to 
repeat  the  same  cadence  for  consecutive  phrases.  In  the 
middle  of  a  melody  a  perfect  cadence  in  the  tonic  key 
should  be  avoided  as  far  as  possible.  From  now  on  the 
student  should  carefully  analyze  the  cadences  in  whatever 
music  he  plavs  or  hears.  The  works  of  Schumann  are 
particularly  rich  in  daring  and  individual  cadence-effects. 
Some  interesting  examples  are  herewith  cited  from  vari- 
ous composers. 


1 62 


Tonal  Counterpoint 


MENDELSSOHN.    "St.  Paul,"  No.  n 


=tiFI 

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f  ' 

..), 

T 

f 

r 

PAINE.  "O3dipus,"   No.  2 


R* 


i^it  J          ^-^jtfJ.                  |  J   JUJ   | 

F^=| 

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r 

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|r  r  Y  r  ''  r  —  ^ 

PAINE.    "  Birds  of  Aristophanes,"   No. 


•  %v«  lower 


f 


**ttt  ? 


f 


Let  us  return  for  a  moment  to  the  version  with  the 
melody  in  the  soprano.  At  (a)  the  third  is  doubled  in 
the  tenor  to  gain  a  fresh  note  at  the  end  of  the  ascending 
phrase,  the  skip  downward  from  c  to  g  being  also  effective. 
It  is  seldom  good  to  have  the  tenor  and  bass  move  so  long 
in  parallel  thirds  as  at  (6) ;  in  this  case,  however,  they  are 
justified  by  the  sequence  in  the  melody,  the  usual  weak 
effect  of  continuous  thirds  being  removed  by  the  fact  that 
the  first  notes  in  each  group  of  quarters  are  accented  pass- 
ing notes  and  form  a  characteristic  dissonance  with  the 
upper  voice. 

§i  10.  The  same  melody  is  now  transposed  into  Bb  minor 
and  placed  in  the  bass. 


Four -Part  Writing 


163 


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This  exercise  has  been  purposely  harmonized  in  simple 
style,  note  against  note.  We  now  take  the  same  bass 
melody  and,  preserving  the  former  harmonic  basis,  con- 
struct short  melodious  phrases  in  the  different  voices. 
This  procedure  has  been  adopted  as  a  model  for  the  stu- 
dent in  his  treatment  of  subsequent  exercises,  and  until  he 
can  rely  upon  his  harmonic  instinct,  working  subconsciously, 
so  to  speak,  it  will  be  found  a  very  helpful  method, 
though  it  must  not  be  allowed  to  degenerate  into  a  mere 
mechanical  formula. 


i 


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164 


Tonal  Counterpoint 


m 


& 


P 


i 


f 


The  above  exercise  is  by  no  means  put  forth  as  perfect 
counterpoint.  The  tenor  is  rather  monotonous  for  a  good 
independent  melody,  and  the  other  voices,  as  the  student 
doubtless  sees  for  himself,  are  constrained  and  awkward 
in  places.  It  is  simply  an  example  of  possibilities  in 
a  rather  limited  field.  At  the  discretion  of  the  teacher 
the  same  melody  may  be  treated  in  the  alto  voice  in  the 
key  of  B  minor,  and  in  the  tenor  in  the  key  of  E  minor. 


EXERCISES 


1. 


1, 

F= 

F= 

- 

\= 

F= 

*= 

- 

^a  f  \  I 

tr~ 


The  same  melody  to  be  placed  in  the  bass  in  the  key  of  F 
major,  in  the  tenor  in  E  major,  and  in  the  alto  in  Ab  major. 
For  the  version  in  the  bass,  in  order  to  allow  a  better 
cadence,  the  last  few  measures  mav  be  altered  as  follows: 


3 


1 


/T\ 


This  melody  may  be  treated  in  turn,  in  the  bass,  key  of 
A  major;  tenor  in  E  major,  and  alto  key  of  Bb  major. 


Four-Part    Writing 


1 6* 


M 


s 


P 


Same  melody  with  motion  of  quarter  notes  in  the  different 


voces  : 


^ 


•  rrOi 


etc. 


The  same  melody  to  be  treated  in  like  manner  in  the  three 
other  voices, —  that  is,  first  in  simple  style,  then  with  mixed 
counterpoint  of  two  notes  against  one  in  the  accompanying 
parts.  Choice  of  key  is  left  to  the  discretion  of  the  stu- 
dent. 

4. 


In  the  harmonization  of  this  melody  suitable  keys  for  the 
different  voices  are  Bb  major  for  the  bass,  D  major  for 
the  alto  and  A  major  for  the  tenor. 

§111.  Very  valuable  practice  is  afforded  in  the  forma- 
tion of  a  flowing  contrapuntal  voice  by  writing  a  bass  part 
of  two  notes  against  one  with  the  melody  in  any  one  of  the 
upper  voices.  Three  examples  of  this  kind  follow. 


Tonal  Counterpoint 


i 


«=•=•& 


i 


No.  2  is  the  same  melody  in  the  alto  with  a  like  treatment 
in  the  bass.  At  (a)  the  fifths  between  tenor  and  bass 
are  saved  by  the  exceptional  change  of  harmony  on  the 
second  beat,  which  sufficiently  diverts  the  attention: 


P 


transposed  from  above 


etc. 


me 


^ 


JIT  mr 


3. 


si 


$T"3  f 


etc. 


1 


^g 


r^    otfo    g 


Four-Part    Writing 


While  working  on  the  above  exercises  the  student  is 
advised  to  look  up  as  models  of  style  for  this  kind  of  writ- 
ing, Choral  No.  164  in  Bach's  "  371  Four-voiced  Chorals," 
and  also  the  second  chorus  in  Mendelssohn's  "  Athalie." 
A  more  elaborate  example  of  a  "  basso  continue  "  may 
be  found  in  the  wonderful  "  Credo  "  of  Bach's  Mass  in  B 
minor,  and  also  in  the  final  elaborate  treatment  of  the  theme 
in  the  Tannhaiiser  March,  Act  II,  Scene  4.  These  and 
analogous  examples  which  the  student  should  search  out  for 
himself  will  repay  careful  study.  As  to  the  actual  render- 
ing of  the  three  exercises  given  above,  we  may  imagine 
voices  in  unison  on  the  melody,  and  the  harmonic  accom- 
paniment played  on  the  organ,  with  the  running  bass  made 
especially  prominent  on  the  pedal. 

SUPPLEMENTARY  EXERCISE 


§112.  These,  and  similar  melodies  should  now  be  worked 
out  with  a  flowing  counterpoint  in  one  of  the  inner  voices. 
It  will  now  be  more  difficult  to  compose  an  interesting  and 
varied  counterpoint,  on  account  of  the  limitations  in  range 
incidental  to  the  inner  position.  Of  course  when  we  come 
to  free  writing  for  strings  and  are  composing  a  flowing  part 
for  the  second  violin  for  example,  we  shall  often  cross  it 
above  the  first  violin  or  below  the  'cello.  In  these  present 
exercises,  however,  the  student  should  avail  himself  of 
this  freedom  somewhat  rarely,  if  at  all.  A  most  valuable 
part  of  the  practice  in  counterpoint  exercises  consists  in 
the  attempt  to  achieve  artistic  results  with  simple  material 
and  with  certain  self-imposed  limitations.  Several  exer- 
cises are  begun,  to  be  completed  by  the  student. 


168 


Tonal  Counterpoint 


• 


i 


efc. 


etc. 


Same  melody  as  No.  3,  §i  1 1  ;  transposed  into  F  major. 


1 


etc. 


B¥» 


Same  melody  as  No.  i,  §m  ;  transp  >sed  into  D  major. 

Occasionally  a  suspended  note  may  be  used  as  at  (a),  but 
with  the  note  struck  again,  not  tied,  in  order  that  the  motion 
mav  not  be  broken. 


^ 


etc 


Ml 


^^ 


Four -Part    Writing 


At  (a)  and  (b]  we  have  purposely  crossed  the  tenor  above 
the  alto,  to  illustrate  the  actual  adoption  of  this  device  for 
extending  the  range  of  an  inner  voice.  At  both  places 
we  are  saved  from  going  over  again  the  same  notes  as  in 
preceding  measures.  The  student  may  now  work  out 
the  same  melody  with  a  flowing  alto  voice,  which  may 
occasionally  cross  above  the  soprano,  or  drop  below  the 
tenor.  This  should  not  be  done,  however,  at  the  first  indi- 
cation of  difficulty,  but  only  when  distinct  advantages 
in  interest  and  variety  are  thereby  gained  for  the  contra- 
puntal part.  As  far  as  possible  one  should  strive  to 
construct  a  good  alto  voice  in  its  normal  position.  The 
exercise  may  begin  as  follows : 

Same  melody  as  above 


§113.  Let  us  now  take  up  the  harmonization  of  some 
of  the  standard  choral  melodies.  In  this  work,  as  soon  as 
possible,  all  the  ingenuity  and  skill  of  the  student  should 
be  expended  upon  the  melodic  independence  of  each  voice. 
At  first,  however,  as  he  will  doubtless  have  to  pay  con- 
siderable attention  to  the  harmonic  basis,  he  should  con- 


7/0 


Tonal  Counterpoint 


tent  himself  with  plain  chords  and  occasional  passing  notes. 
The  chief  aim  should  be  to  secure  firmly  moving  progres- 
sions in  the  bass,  and  in  the  early  stages  of  the  work  there 
should  be  no  attempt  to  make  the  inner  voices  elaborate. 
To  illustrate  the  general  style  of  treatment,  we  now  har- 
monize a  choral.  The  one  selected  is  the  German  choral 
"  Freue  dich,  O  meine  Seele  ": 


The  cadences  are  plainly  indicated  by  the  holds,  and  it  is 
always  best  for  the  student  to  sketch  these  in  first.  When 
the  first  line  is  repeated,  as  is  often  the  case,  the  repetition 
should  be  written  out  and  new  effects  of  cadence  and  of 
modulation  introduced.  It  is  seldom  good  in  any  form 
of  composition  to  repeat  a  phrase  or  period  literally;  the 
attention  and  interest  of  the  hearer  should  always  be  pre- 
served by  some  change  of  harmony  or  some  new  touch  of 
rhythm.  At  the  end  of  the  first  phrase  it  is  obvious  that 
there  may  be  either  a  plagal  cadence  in  the  key  or  an 
authentic  cadence  in  the  key  of  the  dominant.  As  the  latter 
is  the  more  varied,  we  save  it  for  the  repetition.  Note  that 
in  general  the  mediant  in  the  melody  will  demand  tonic  har- 
mony. At  (a) ,  however,  variety  is  gained  by  a  modulation 
to  the  dominant  of  the  relative  minor.  The  other  cadences 
need  no  explanation  save  the  one  at  (b).  Here,  after  the 
modulation  into  a  minor,  we  have  somewhat  exceptionally 
used  the  last  beat  of  the  measure  for  a  return  to  the  main 
key.  The  cadences  selected  are  written  out  in  close  score. 


e:     f  a:  V    I 

V  *.' 

*  The  natural  hiatus  between  the  phrases  re*noves  all  bad  effect  from  the  cross- 
relation. 


Four-Part    Writing  I-JL 

The  student  will  readily  understand  the  following  simple 
version  without  anv  comments. 


Observe  that  the  last  note  of  the  melody  is  lengthened 
and  a  free  ending  added.  This  is  often  done  by  Bach,  Men- 
delssohn and  others  in  their  treatment  of  choral  melodies, 
and  the  practice  may  be  adopted  by  the  student,  as  he 
will  thereby  be  afforded  a  valuable  opportunity  for  the 
exercise  not  only  of  his  fancy  but  of  his  good  taste.  An 
instructive  example  of  this  form  of  ending  may  be  found 


172 


Tonal  Counterpoint 


in  the  choral  "Sleepers,  Wake,"  from  Mendelssohn's  "  St. 
Paul."  These  extended  endings  (almost  invariably  with  a 
pedal  point  in  one  voice  or  in  several  at  once)  are  by  no 
means  limited  to  vocal  music.  Very  interesting  examples 
of  their  use  may  be  found  in  the  following  preludes  and 
fugues  from  the  "Well-Tempered  Clavichord": 

Prelude  No.  IX,  Book  I 


For  a  more  elaborate  modern  example  see  the  following 
passage  in  Brahms'  variations  for  orchestra  on  a  choral 
theme  by  Haydn: 

Variation  No.  3 


§114.  We  now  give  for  analysis  two  different  harmoni- 
zations of  the  same  choral  taken  from  the  works  of  Bach. 


Four-Part   Writing 


173 


The  first,  composed  of  simple  chords,  is  largely  harmonic 
in  style,  though  the  inner  voices  are  by  no  means  devoid 
of  interest.  The  second,  with  its  wonderful  florid  part- 
writing,  may  be  considered  as  the  style  towards  which,  in 
general,  the  student's  work  should  tend.  For  some  time, 
however,  his  attempts  will  look  far  more  like  the  former 
example,  and  rightly  so. 

BACH.     "Johannes  Passion  " 

4nh* 


3 


m 


ipPp 


m 


c\ 


w 


o 


P 


/7\ 


PPi 


c\ 


K\ 


m 


In  this  version  the  following  points  are  especially  worthy 
of  notice :  The  varied  range  and  sturdy  swing  of  the  bass ; 
the  repeated  notes  in  the  tenor  at  (a),  which  would  seem 


Tonal  Counterpoint 


to  justify  its  derivation  (teneo,  I  hold);  likewise  the  sus- 
tained alto  part  at  (6) ;  and,  lastly,  the  rather  unusual  modu- 
lation into  the  subdominant  at  (c). 

BACH.    Cantata,  "  Sehet,  wir  gehen  hinauf  " 


I  J.,  „  I  I  .  I 

CT   ^hrJ-T?? 


^^^ 


fc 


^ 


ID  !> 


s 


a 


^a 


^ 


»-• 


5^ 


*=c 


§s 


p 


/O 


^ 


/7\ 


? 


In  this  example  the  student  should  play  through  each  of 
the  four  voices  by  itself  and  observe  their  extraordinary 
variety  and  range  of  movement.  The  choral  is  a  com- 
bination of  four  separate  melodious  parts,  in  which  there 
are  hardly  any  repeated  notes;  only  once  in  the  tenor  at 


Four -Part  Writing 


175 


(a)  and  once  in  the  alto  at  (6).  Note  that  at  two  places, 
(c}  and  (d),  the  range  of  the  inner  voice  has  been  widened 
by  crossing.  Even  the  bass  is  once  for  a  moment  crossed 
above  the  tenor  at  (e).  The  use  of  anticipations  in  the 
bass  shown  at  (/)  is  rather  rare,  though  common  in  an  upper 
part.  Among  manifold  points  of  melodic  interest  in 
this  beautiful  choral  which  the  student  may  discover  for 
himself,  the  majestic  sweep  of  the  bass  in  the  ascending 
diatonic  passage  of  the  opening  measures  is  especially 
noteworthy. 

EXERCISES 


Chorals  to  be  harmonized. 

"  Christus  der  ist  mein  Leben." 

c\ 


1. 


"  Mach's  mit  mir  Gott,  nach  deiner  gut." 


Nun  danket  alle  Gott 


Auf  meinem  lieben  Gott 


"  Wer  nur  den  lieben  Gott  lasst  walten." 


176 


Tonal  Counterpoint 


"  Xun  ruhen  alle  Waldern." 

/T\ 


Erhalt  uns,  Herr,  bei  deinem  Wort." 


"  Mein  Augen  schliess'   Ich  jetz." 


-fajijjjJipm 


"  Schmiicke  dich,  O  Hebe  Seele." 


"Allein  Gott  in  der  Hoh',  sei  Ehr." 


io.|,'i.airrrrirJprir^r  ^i^^ 


f  rp  I 

I I 1 


0   Haupt  voll   Blut  und  Wunden. 


11. 


Four -Part  Writing 


I77 


"Gott  erhalte  Franz  den  Kaiser." 


12 


Bin  feste  Burg  ist  unser  Gott." 


13 


§115.  We  now  give  some  short  and  simple  melodies  to  be 
harmonized  in  contrapuntal  style  for  four  stringed  instru- 
ments, —  first  and  second  violin,  viola  and  'cello.  Although 
we  shall  not  expect  these  exercises  to  exemplify  all  the 
subtle  points  of  detail  in  effective  writing  for  strings  (for 
this  it  will  be  necessary  to  wait  until  we  come  to  speak  of 
homophonic  style  and  its  relation  to  writing  for  string 
quartet),  still  it  is  well  for  the  student  thus  early  to  do 
some  simple  four-part  writing  with  strings  in  his  mind  as 
the  means  of  performance.  The  chief  method  of  learn- 
ing how  to  write  for  strings  is  to  practise  writing  for  them. 
Even  in  the  simplest  style  we  are  freed  from  certain  limi- 
tations of  vocal  writing,  and  we  gain  many  advantages. 
The  fact  that  there  need  be  no  consideration  of  words  en- 
ables us  at  once  to  make  the  rhythm  of  the  parts  much  more 
varied  and  contrasted.  In  music  written  to  words  it  is 
necessary,  in  general,  that  all  the  voices  should  sing  the  same 
word  or  syllable  at  the  same  time,  though  often  one  voice 
may  sing  a  word  to  a  note  of  a  certain  length,  while  other 
voices  have  flowing  parts  of  two,  three  or  four  notes  to 
the  same  word.  This,  however,  can  only  be  done  with 
certain  words.  Only  in  the  most  florid,  fugal  style  of  Bach 
are  all  the  voices  singing  in  different  rhythms  for  a  long 
time,  and  if  this  style  were  attempted  by  a  novice,  a  mere 
jumble  of  syllables  and  notes  would  be  sure  to  result.  But 
in  writing  for  strings  the  utmost  freedom  and  contrast  in 
rhythm  is  possible.  In  fact,  our  aim  should  be  to  give 
each  part,  as  far  as  possible,  a  distinct  rhythm  of  its  own 


Tonal  Counterpoint 

and  at  the  same  time  to  keep  the  writing  natural.  Good 
writing  is  never  labored  or  constrained.  Likewise  we 
need  not  consider  the  breathing;  a  stringed  instrument 
can  sustain  a  note  as  long  as  it  is  desirable  for  it  to  be 
heard.  Again,  the  range  of  strings  is  far  greater  than  that 
of  voices.  At  first,  however,  the  student  is  advised  in  this 
respect  to  treat  his  instruments  like  "idealized"  human 
voices,  and  not  to  write  at  length,  either  in  the  highest  or 
lowest  part  of  the  compass.  For  practical  purposes  the 

range  of  the  'cello  may  be  said  to  be  from 


of  the  viola,  from 


of  the  second  violin,  from  (fo       /(' 


and  of  the  first  violin,  from 

SB 
•5 

Strings  can  also  move  at  a  far  greater  speed  than  voices, 
hampered  as  the  latter  are  by  the  fact  that  the  words  must 
be  distinctly  pronounced.  Bolder  leaps  may  also  be  taken 
by  strings  and  more  chromatic  intervals  used,  though  at 
first  the  student  is  earnestly  cautioned  against  the  use  of 
strange,  unmelodic  intervals  until  he  has  acquired  the  cul- 
tivated judgment  to  know  just  when  some  special  effect 
is  worth  while.  He  is  by  no  means  expected  to  introduce 
at  once  all  the  complicated  chromatic  chords  he  may  know. 
Only  little  by  little  will  his  work  for  strings  look  very  dif- 
ferent from  that  for  voices.  From  the  very  outset,  how- 
ever, his  eye  must  be  trained  to  read  that  form  of  open 
score  peculiar  to  writing  for  strings.  The  'cello  which 

plays  the  bass,  is  written  either  on  the  F  clef  .9' 


or  that  which  has  middle  C  here, 


according  as  the  position  is  low  or  high;  the  viola,  which 


Fo ur-  Part  Writing 
plays  the  tenor,  is  written  on  the  clef  which  has  middle  C 
on  the  third  line;  that  is    ||^ 

while  both  the  second  violin  and  the  first  violin,   which 
play  the  alto  and  soprano  parts,  respectively,  are  written 

on  the  G  or  so-called  violin  clef;  that  is, 

The  chord  of  C  major  written  in  open  position  will  now 
look  like  this: 


Cello 


§116.  We   now  take  the  following  short   melody  from 
Gluck  and  harmonize  it  for  strings: 

GLUCK 


It  is  obvious  that  the  simplicity  of  the  theme  will  demand 
a  simple  style  of  treatment,  and  we  shall  use  nothing  but 
the  harmonies  inherently  implied  by  the  melody  itself. 
At  the  same  time  we  shall  try  to  make  all  the  parts  as 
interesting  as  possible,  and  strive  particularly  for  variety 
of  rhythm. 

1$  Violin 


£ 


r  rrrr 


F^ 


2*  Violin. 


ioji 


Cello 


^ 


i8o 


Tonal  Counterpoint 


In  this  example,  simple  as  it  is,  the  student,  by  playing 
over  the  several  parts,  will  see  that  each  one  has  a  distinct 
rhythm  of  its  own  which,  as  far  as  possible,  is  made  to 
contrast  with  that  of  any  one  of  the  three  other  voices  in 
a  given  measure.  In  fact,  in  only  three  places  do  two 
voices  have  the  same  rhythm.  In  the  second  measure  the 
alto  and  bass  are  alike;  in  the  third,  the  soprano  and  tenor, 
and  in  the  next  to  the  last  the  two  inner  voices.  In  the 
fourth  and  fifth  measures  notice  how  effective  are  the  sus- 
tained notes  in  the  tenor  and  alto.  At  (a)  mark  the  pleas- 
ing effect  of  dissonance  caused  by  the  accented  passing 
note  c  in  the  alto  heard  against  the  c#  in  the  bass. 

§ 1 1 7.  We  now  treat  in  like  manner  the  following  melody 
from  Schubert: 


As  the  melody  in  itself  is  more  varied  rhythmically  than 
the  preceding,  we  shall  use  a  more  florid  style.  The  melody 
is  also  periodic,  as  the  student  will  see  on  playing  it  over 
and  counting  the  measures.  It  is  an  eight-bar  sentence 
expanded  into  ten.  As  the  student  who  has  studied  "  mu- 
sical form"  will  know,  one  of  the  very  best  ways  of 
marking  the  subdivisions  of  a  musical  sentence  is  by  modu- 
lations into  related  keys.  So  at  the  fourth  measure,  as 
the  melody  allo'ws  it,  we  shall  make  the  time-honored  mod- 
ulation into  the  dominant;  and  at  measures  2  and  7,  the 
a#'s  in  connection  with  the  d's  following  will  naturally 


Four-Part  Writing 


181 


lead  us  into  the  related  and  yet  contrasting  key  of  B  minor. 
Although  these  exercises  are  written  for  strings,  nothing 
as  yet  has  been  said  about  "  bowing"  and  the  special  marks 
of  phrasing  which  are  always  indicated  in  writing  for 
stringed  instruments.  It  has  been  thought  best  to  reserve 
this  important  feature  for  a  later  chapter,  in  which  the 
more  intricate  points  in  writing  for  strings  will  be  explained. 
For  the  present  it  is  understood  that  all  the  parts  are  to 
be  played  legato,  with  the  natural  phrasing  any  violinist 
would  instinctively  use,  except  where  the  special  effects  of 
staccato  or  of  pizzicato  are  marked.  The  professional 
musician  will  readily  condone  this  omission. 


182 


Tohal  Counterpoint 


After  an  analysis  of  this  illustration,  which,  indeed,  is 
distinctly  vocal  in  the  smooth,  melodic  flow  of  the  parts, 
the  student  will  understand  more  clearly  the  meaning  of  the 
statement  that  in  general  it  is  possible  to  make  the  rhythm 
freer  and  more  varied  in  writing  strings  than  for  voices. 
If  the  above  melody  were  to 
gencies  of  the  words  would  t> 
florid  style  could  we  have  the  c 


sung  by  voices,  the  exi- 

.uch  that  only  in  a  very 

/asts  we  have  made.     In 


the  eighth  measure,  for  instance,  the  second  violin  holds 
a  note  for  five  beats,  while  each  of  the  other  parts  has  a 
different  rhythm. 


EXERCISES 

§118.  Whenever  the  following  exercis* 
character  and  have  notes  of  different  ler. 
before  working  them  out  should  play  each  .  _,  trough 

carefully,  and  as  far  as  possible  decide  "  ehand  just 
which  notes  he  will  treat  as  harmony  noteb,  and  which  as 
passing  notes  (both  unaccented  and  accented;,  or  as  aux- 
iliary notes.  In  this  matter  it  is  impossible  to  state  any 
hard-and-fast  rule  as  to  which  notes  should  be  treated  so  as 
to  outline  the  harmony.  In  general,  those  notes  should  be 
selected  which  give  the  strongest  harmonic  progressions, 
and  very  seldom  should  each  note  of  the  melody  be  har- 
monized with  a  different  chord.  Much  depends,  of  course, 
upon  the  speed  of  the  music.  At  a  rapid  tempo  the  har- 
monic changes  need  not  be,  in  fact  ought  not  to  be,  so  fre- 
quent as  at  a  slow  tempo,  when  it  is  generally  very  we?k 
and  monotonous  to  continue  the  same  chord  or  relat  1 
chords  through  many  notes  of  the  melody.  In  this  imp( 
tant  particular  the  student  must  strive  to  cultivate 
true  harmonic  instinct,  and  must  follow  carefully  the  cri 
cisms  and  recommendations  of  his  teacher. 


Larghetto 


MOZART 


Four -Part  Writing 


183 


A  ndante 


BEETHOVEN 


The  student  will  find  valuable  practice  to  treat  the 
above  melody  twice.  Fir,-.~g:in  simple  style,  in  which  case 
the  first  phrase  might  be-' somewhat  as  follows: 


Anda       con  nioto 


IF'     £=*=£ 

rl  —  h 

J.    J; 

* 

{  *  J     1 
•u  i    i  —  v 

** 

^-~«_ 

™ 

«-.i^  —  4  * 

-  —  ?  — 

ij*-**  —  *  

-  F 

Afterwards  a  more  florid  version  may  be  made,  in  which 
the  motion  of  four  sixteenths  to  a  beat  is  to  be  kept  up  in 
some  one  of  the  parts.  The  last  note  of  the  melody  may 
be  prolonged,  and  the  student  may  try  his  hand  at  an 
el  borate  ending. 

The  following  measures  will  indicate  the  general  style  of 

s  setting: 


'ante 


Tonal  Counterpoint 


SCHUBERT 


In  working  out  these  exercises  the  student  should  con- 
stantly strive  to  secure  freedom  and  individuality  by  the 
use  of  accented  passing  notes,  suspensions,  appoggiaturas, 
etc.,  and  especially  should  he  kindle  his  enthusiasm  and 
improve  his  style  by  looking  up  examples  of  free  writing 
for  strings  in  the  works  of  the  great  composers.  A  few 
illustrations  are  cited. 

Adapted  from  Chadwick's  "  Harmony" 


^ 


1 


g 


From  Schubert's  Quartet  in  D  minor. 

Andante  con  moto 


tt 


pp 


Four-Part  Writing 


rfecresc, 


^ 


m 


cresc. 


HES 


\r\   »• 


m 


This  wonderful  example  of  writing  for  strings  should 
be  carefully  studied  and  each  voice  sung  throughout. 
Although  it  is  entirely  without  variety  of  rhythm,  yet  the 
chords  are  grouped  so  artistically  that  the  effect  is  one  of 
perfect  beauty. 


Intermezzo 


i86 


Tonal  Counterpoint 


This  beautiful  movement  from  Schumann's  String  Quar- 
tet in  A  minor,  quite  apart  from  aesthetic  considerations, 
affords  a  most  inspiring  model  of  style  for  the  student,  for 
it  abounds  in  suspensions,  syncopations,  accented  passing 
notes  and  subtle  chromatic  effects. 


*  At  (a)  and  (6)  let  the  parallel  fifths  be  accounted  for. 


CHAPTER   IX 


Double  Counterpoint 

§119.  It  is  necessary  now  to  learn  something  of  that 
form  of  counterpoint  known  as  "  double  counterpoint," 
not  only  because  its  practice  affords  valuable  mental  train- 
ing, but  because  it  is  an  integral  part  of  the  structure  of 
such  common  forms  of  composition  as  the  pianoforte  in- 
vention, the  fugue,  and  in  most  cases  of  the  sonata  and  of 
the  symphony.*  Furthermore,  a  free  and  incidental  use 
of  double  counterpoint  is  often  made  where  the  average 
listener  would  not  recognize  it  as  such,  although  he  might 
be  aware  of  some  carefully  planned  design  in  the  harmonic 
structure.  In  Sullivan's  well-known  hymn  tune,  "  On- 
ward, Christian  Soldiers,"  for  instance,  the  sopranos  and 
the  tenors  answer  each  other  in  double  counterpoint. 

t  . 

B 


.i 


1 


m 


Likewise  in  the  opening  measures  of  Chopin's  Ballade  in 
A!>  major  there  is  free  double  counterpoint  between  two 
of  the  voices;  for  example, 


A 

m 


two 
measures 


§120.  By  double  counterpoint,  therefore,  we  mean  "  in- 
vertible  counterpoint  " ;  that  is,  when  two  melodies,  written 
to  be  played  or  sung  together,  are  capable  of  inversion, 
either  being  above  or  below  the  other,  they  are  said  to  be 

*  In  almost  any  symphony  may  be  found  interesting  examples  of  double  coun- 
terpoint. The  first  movement  of  Tschaikowski's  Sixth  Symphony  is  suggested  as 
a  movement  likely  to  inspire  the  student.  The  first  and  second  movements  of 
Brahms'  Second  Symphony  are  also  rich  in  examples. 

187 


Tonal  Counterpoint 


in  double  counterpoint.  The  inversion  may  take  place  at 
any  interval,  but  the  two  kinds  which  are  most  used,  and 
are  of  the  greatest  practical  advantage  to  the  student,  are 
double  counterpoint  at  the  octave  and  at  the  fifteenth. 
Double  counterpoint  is  also  triple  or  quadruple,  according 
as  we  have  a  combination  of  three  or  four  melodies,  any 
one  of  which  may  be  the  highest,  the  lowest,  or  an  inner 
part.  In  this  brief  manual  we  shall  treat  only  of  double 
counterpoint  at  the  octave  and  the  fifteenth,  for  two  or 
for  three  voices.  Those  who  are  interested  in  double 
counterpoint  at  the  less  usual  intervals  are  referred  to  the 
exhaustive  treatises  of  Dubois,  Prout  and  Bridge. 

§121.  Double  counterpoint  at  the  octave  and  at  the 
fifteenth  are  virtually  identical  as  far  as  harmonic  consid- 
erations are  concerned,  the  only  practical  difference  being 
one  of  position;  that  is,  in  double  counterpoint  at  the 
octave  the  two  melodies  in  their  first  grouping  are  not  to  be 
more  than  an  octave  apart,  and  the  inversion  is  made  by 
placing  the  original  lower  voice  up  an  octave,  or  the  orig- 
inal higher  down  an  octave,  while  in  either  case  one  voice 
remains  as  it  is:  for  example, 


H  A  v  D  x  . 


Creation  ' 


A                       9 

r    r  cr 

L 

^ 

-^ 

LJ.  _LJ  —  ! 

In  this  example  the  inversion  is  made  by  placing  the 
original  melody  up  an  octave,  while  the  contrapuntal 
voice  retains  its  original  position. 


Subject 


HANDEL.    Te  Deum  in 


=f=£ 

=3= 

-N        ^ 

3 

^ 

r  '" 

Inversion 

^ 

1         Ll 

;t* 

i^ 

^ 

Double  Counterpoint 


189 


In  the  above  example,  on  the  other  hand,  the  upper  voice 
is  placed  an  octave  below.  Observe  in  both  these  exam- 
ples that  the  distance  of  an  octave  between  the  subject  and 
the  counterpoint  is  never  exceeded.  In  double  counter- 
point at  the  octave,  whenever  the  two  voices  in  the  original 
grouping  are  more  than  an  octave  apart,  no  real  inversion 
can  take  place  by  the  change  of  only  one  of  the  voices,  but 
merely  a  contraction;  for  example,  suppose  that  we  wish 
to  invert  the  following  phrase 


by  placing  the  lower  voice  an  octave  higher.  As  the 
voices  at  *  exceed  the  interval  of  an  octave,  it  is  evident 
that  here  no  inversion  can  be  made;  for  example, 


e  *B 

y  Jj     I   ' 

(fr>  4 

tJ                   H 

-     *  •  J 
# 

Iftn  *  JIJ-J-J 

*J            W** 

^'              ^ 

Here   the  latter  part  of  voice  A  is  still  above  voice  B, 
although  the  distance  between  the  voices   is  contracted 


from 


The  objection  is  sometimes  made  to  double  counterpoint 
at  the  octave  that  the  limitation  of  range  hampers  effective 
writing,  —  that  the  necessity  for  not  exceeding  the  dis- 
tance of  an  octave  between  the  parts  is  fatal  to  freedom 
of  movement.  Doubtless  this  is  true  to  some  extent,  yet 
as  Handel  in  the  chorus,  "We  worship  God,"  in  "Judas 
Maccabseus, "  did  not  seem  to  be  fettered  by  the  limitation, 


igo 


Tonal  Counterpoint 


or  Mozart  in  his  Mass  in  C  minor,  it  will  be  well  for  the 
student  in  early  exercises  to  cultivate  his  ingenuity  by  the 
formation  of  a  melodious  counterpoint  without  exceeding 
the  limit  of  an  octave. 

HANDEL.     "Judas  Maccabaeus  " 
* 


* 


MOZART.    Mass  in  C  minor 


§122.  In  double  counterpoint  at  the  fifteenth  (double 
octave),  the  inversion  is  ordinarily  made  by  raising  the 
lower  voice  an  octave  and  at  the  same  time  lowering  the 
upper  an  octave.  As  a  result,  the  position  of  the  voices 
is  often  much  better  than  if  only  one  had  been  changed, 
and  in  the  original  grouping  the  limit  of  an  octave  need 
not  be  preserved;  for  example,  in  the  following  phrase, 


as  the  two  voices  are  sometimes  more  than  an  octave  apart, 
it  is  clear  that  no  continuous  inversion  can  be  made  by 
lowering  the  upper  voice  an  octave  or  by  raising  the  lower. 
If  the  upper  voice  is  lowered  two  octaves,  the  register  is  too 
low,  while  if  the  lower  is  raised  two  octaves,  it  is  too  high. 
By  moving  each  voice  an  octave,  however,  and  in  oppo- 
site directions,  a  perfect  inversion  is  secured  and  both 
voices  are  in  a  convenient  position;  for  example, 


*  Let  the  student  write  out  the  inverison  for  each  of  these  examples. 


Double   Counterpoint 


191 


te 


eas 


e/r 


£f 


Some  examples  are  now  cited  of  phrases  in  double  coun- 
terpoint at  the  fifteenth. 

BEETHOVEN.    Mass  in  D 


1. 


3S 


Inversion 


3h  >  *l  - 


>i>..  r? 
ft^tEE 


^ 


pp 


2=$ 


ALBRECHTSBERGER 


Inversion 


j  fy  "  *  J  "  = 

^-— 

^*«, 

=f=l 

^^ 

1    [     U 

In  the  above  example  observe  that,  althotigh  the  two 
voices  are  within  the  range  of  an  octave,  the  inversion  is 
made  by  transposing  each  voice,  just  as  if  the  original 
grouping  had  been  made  with  reference  to  double  o 
terpoint  at  the  fifteenth.  This  plan  is  often  adopted. 


I92 


Tonal  Counterpoint 


HAYDN 


Inversion 


Inversion 


HANDEL 


rtA,.      •         l 

1  j  p  r  r  r  r  f^ 

—  -JB  

\Kii^'~  f  r  M 

I^F 

Hi 

i"        r    i 

H  —  I 

r^ 

l~to  

___£ 

e 

=g=      ^  ^ 

X.  B.  —  In  the  above  example  (No.  4),  to  gain  a  special 
vocal  effect,  the  upper  voice  is  lowered  two  octaves. 


MOZART.    Fugue  for  Orchestra 


5. 


0 

** 

Inversion 

nHi—  ?  1 

J  J^dl 

Trrr' 

i  rj^i 

«J           *  ^-^ 

J^JJ 

jjjj 

o 

§123.  When  the   above  examples    have  been   analyzed 
it  will  be  evident  that  they  greatly  resemble  in   general 


Double  Counterpoint 


193 


appearance  the  previous  exercises  in  simple,  two-part  coun- 
terpoint. The  student  is  far  too  likely  to  think  of  double 
counterpoint  as  something  recondite  or  almost  cabalistic. 
This  is  by  no  means  the  case.  Very  often  counterpoint 
written  with  no  reference  to  the  rules  of  double  counter- 
point is  yet  perfectly  capable  of  inversion.  This  statement 
may  be  verified  by  referring  back  to  examples  in  Chapter  IV. 
In  fact,  the  arbitrary  restrictions  to  be  observed  in  writing 
double  counterpoint  are  few  and  simple,  and  we  shall  see 
clearly  just  what  these  limitations  are  if  we  compare  all 
the  intervals  within  the  octave  with  their  inversions. 

*•  * 


Intervals:  i,  2 
(4,  5),  6,  7, 


2 

* 

•«*• 

•*»    •»• 

* 

•*»•   -•• 

^-s- 

-o  »- 

= good 


Inversions:  8,7,6 

(5,   4),    3,   2,   i. 

It  is  evident,  on  examination  of  this  chart,  that  thirds 
and  sixths  invert  in  a  satisfactory  manner.  Likewise  the 
unison  and  the  octave,  although  they  should  not  be  em- 
ployed often  in  two-part  writing,  except  on  the  first  and 
last  notes  of  an  exercise.  As  the  intervals  seconds  and 
sevenths  are  of  no  harmonic  significance  in  two-part  writ- 
ing, they  may  be  left  out  of  consideration.  Our  atten- 
tion, therefore,  is  centered  upon  fifths  and  fourths,  and 
these  intervals  chiefly  require  the  student's  care. 

§  1  24.  Consecutive  perfect  fifths  are,  of  course,  forbidden, 
and  consecutive  perfect  jourths  are  equally  objectionable,  as 
upon  inversion  they  become  perfect  fifths.  Even  a  single 
interval  of  a  perfect  fifth  is  practically  never  used  in  double 
counterpoint  except  on  the  accented  beats  as  a  disso- 
nance regularly  prepared  and  resolved,  or  on  the  weak  beats 


as  a  passing  note;  for  example,  not 


in  the  inversion  of  which  the  empty  fourth 


with    a    leap   in   the   lower 
voice  is  too  prominent,  but 


which  inverts  smoothly  into 


Tonal  Counterpoint 


The  following  chart  illustrates  other  correct  and  effective 
uses  of  the  fifth  and  of  the  fourth. 


t 


Inversions 


Of  these  examples,  (a),  (b)  and  (f)  are  self-explanatory. 
At  (d)  we  see  a  fifth  used  as  an  accented  passing  note,  and 
at  (/)  a  fourth  is  introduced  even  on  an  accented  beat, 
where  it  is  clearly  an  unessential  note  —  an  appoggiatura. 

§125.  The  augmented  fourth,  however,  and  its  inversion, 
the  diminished  fifth,  may  be  freely  used  on  accented  or 
unaccented  beats;  for  example, 


Q    ,   * 

PP 


TTTT 


A  perfect  fifth  followed  by  a  diminished  fifth,  resulting 
when  inverted  in  a  perfect  fourth  followed  by  an  aug- 
mented fourth,  should  not  be  used  in  double  counterpoint 
in  two  voices.  The  empty  intervals  are  too  prominent  in 
the  outer  voices;  for  example, 

(a)  (b) 


r8r 


Neither  (a)  nor  (6)  is  good  in  two-part  writing;  (6)  might  be 
altered  into 


Double  Counterpoint 


195 


In  this  case,  the  g  being  a  passing  note,  the  grammar  is 
perfectly  correct.  In  three-part  writing,  however,  when 
the  objectionable  intervals  are  between  an  inner  and  an 
outer  voice,  these  fourths  and  fifths  may  be  freely  intro- 


duced: for  example, 


§126.  The  augmented  sixth  is  not  available  for  double 
counterpoint  in  two  parts  on  account  of  the  unsatisfactory 
effect  of  its  inversion,  the  diminished  third:  for  example, 


I 


§127.  The  diminished  seventh,  however,  may  be  used 
if  care  be  taken  in  the  resolution;  that  is,  if  one  of  the 
notes  which  form  the  interval  be  resolved  before  the  other  : 
for  example, 


The  diminished  seventh  must  not  be  resolved  to  a  fifth 
upon  an  accented  beat,  on  account  of  the  fourth  resulting 

Inversion 


from  the  inversion:  for  example 


§128.  The  student  should  now  look  up  for  himself 
examples  of  double  counterpoint  from  the  works  of  the  great 
composers.  In  this  way  he  will  form  a  good  style  far  more 
quickly  than  by  merely  reading  the  rules.  A  few  well- 
known  passages  are  cited. 

LEO.    "  Kyrie  " 


196  Tonal  Counterpoint 

Inversion 


hiu  4  1  J 

& 

i          /"J 

i5 

4^ 

B 

-     j. 

X" 

V 

W*>     *  ' 

L^y 

—  LU- 

tUf= 

=t=d 

HANDEL.    "  L' Allegro' 


rrrrr  r 


Inversion 


i 


HANDEL.    Anthem 


P 


Inversion 


(a) 


§129.  In  the  above  example  there  are  certain  liberties, 
often  to  be  found  in  free  contrapuntal  writing.  At  (a)  a 
passing  modulation  is  introduced,  and  in  the  inversion  the 


Double   Counterpoint 


T-97 


passage  is  lengthened  by  the  insertion  of  an  extra  measure 
(6).  Observe  particularly  the  contrast  in  rhythm  between 
the  voices. 


A  ndante 


HAYDN*.     Symphony  in  D 


§130.  Of  this  passage  the  first  eight  measures  are  in 
simple  two-part  harmony,  though  in  the  orchestral  score 
each  part  is  doubled  in  the  octave.  At  (6)  the  voices  are 
strictly  inverted,  and  inner  parts  (not  quoted)  are  added 
to  vary  and  strengthen  the  effect. 

§131.  A  charming  example  of  double  counterpoint  may 
be  found  in  No.  VII.  of  Mozart's  Pianoforte  Variations  on 
"  Uiiser  dummer  Pbbel  meint."  See  also  the  following  from 
Beethoven: 


ig8 


Tonal  Counterpoint 


BEETHOVEN.    Quartet  in  C  minor,  Op.  18,  No.  4 


§133.  In  the  scherzo  of  Beethoven's  Pianoforte  Sonata, 
Op.  26,  may  be  found  an  excellent  example  of  double  coun- 
terpoint. The  student  can  easily  look  up  the  passage  for 
himself.  It  begins  as  follows: 


§134.  Likewise  in  the  first  movement  of  Beethoven's 
Sonata  in  D  Minor  (Op.  31,  No.  2)  and  in  the  finale  of  the 
Sixth  Sonata  there  may  be  found  most  inspiring  examples 
of  double  counterpoint. 

§135.  Finally  in  Bach's  Passacaglia  in  C  Minor  for  the 
Organ  there  are  most  wonderful  and  elaborate  passages  in 
double  counterpoint  that  will  repay  careful  analysis. 

§136.   Examples  in  free  pianoforte  style: 

SCHUMANN.    "  Nachtstiicke,"  No.  2 


Double  Counterpoint 


SCHUMANN.     "  Kreisleriana,"  No.  2 


§137-  In  order  to  illustrate  the  suggestions  set  forth  in 
§§123-127,  we  now  work  out  a  few  simple  two-part  exer- 
cises in  double  counterpoint.  Many  of  these  exercises 
should  be  thought  of  as  written  for  different  combinations 
of  strings, —  violin,  viola,  and  'cello.  Not  only  do  they 
sound  better  when  played  on  these  instruments  rather 
than  on  the  pianoforte,  but  valuable  practice  is  gained  in 
the  use  of  the  special  alto  and  tenor  clefs. 

i.  To  the  following  subject  we  are  to  write  below  a 
double  counterpoint  in  the  octave. 

Viola 


As  the  inversion  is  to  be  in  the  octave,  the  counterpoint 
must  never  be  more  than  an  octave  below  the  subject. 
The  counterpoint  must  be  not  only  a  good  bass  to  the 


200 


Tonal  Counterpoint 


subject,  but  a  melody  which  will  be  good  when  placed 
above.  Variety  of  rhythm  between  the  two  voices  is  espe- 
cially to  be  sought,  —  that  is,  when  the  subject  has  long 
notes  the  counter  melody  must  be  animated  and  flowing; 
on  the  other  hand,  when  the  subject  moves  along,  the 
counterpoint  must  either  move  faster  or  else  be  sustained. 
Viola 


£P 


Cello 


=  

i    .Jt            —  jp-i 

—  0— 

=1=^ 
=rf¥l 

Cfrf  P  r 

L_i  — 

J—  i- 

^    i 

Note  carefully  the  contrasts  in  rhythm  that  are    evident 
both  to  the  eye  and  the  ear. 

2. 
Violin 


Double  Counterpoint 


201 


The  only  special  points  to  be  observed  in  this  exercise  are 
the  passing  modulations  into  related  keys.  At  (a)  the 
accented  passing  note  is  effective. 

3. 

Viola 


Cello 


7*^ 


Viola 


m 


In  this  example  in  the  minor  mode,  observe  the  smooth 
resolution  at  (a)  of  the  diminished  seventh.  At  (b)  we 
use  the  melodic  minor  scale. 

§138.  It  is  by  no  means  advisable  to  think  of  all  these 
exercises  as  if  they  were  for  strings.  Double  counterpoint 
is  extremely  useful  and  effective  in  compositions  for  the 
pianoforte,  and  some  of  these  melodies  should  be  treated 
with  reference  to  performance  upon  that  instrument.  In 
two-part  writing  for  the  pianoforte  it  is  generally  better 
not  to  have  the  voices  near  together;  that  is,  neither  both 
Jii^li  nor  both  law,  but  to  place  the  voices  so  that  both 
registers  of  the  instrument  are  used,  the  upper  for  the 
right  hand  and  the  lower  for  the  left.  This  arrangement 
makes  for  a  greater  sonority  of  tone.  Fpr  example,  to  the 
following  subject : 


Let  us  write  a  counterpoint  tu'o  octaves  below,  and  then 
make  the  inversion  by  altering  the  position  of  each  voice. 


202 

Moderate 


Tonal  Counterpoint 


v 

Pianoforte 


g^ 


At  (a)  we  see  an  example  of  a  chromatic  passage  whic? 
in  general,  is  of  good  effect  if  introduced  with  discretii 
in  pianoforte  writing.     In  vocal  counterpoint  such  a  pat- 
sage  would  be  questionable.     We  now  invert  by  placing 
the  upper  voice  two   octaves  below,   and  the  lower  the 
same  distance  above. 

Inversion 


ff 

ttj»k»0 

i  P  rpft 

_  / 

"J 

-f-f-i 

P3^     3 

55F 

S 

' 

'-"  6 

-G 

rrj 

i  —  ^ 

>s 

L^  **ti"  ' 

f\     i 

hP  —  m  ^  ~  —  fif    Jf^f 

£o  n     o    ini 

«r 

' 

H 

-t-f  

= 

r&= 

-  —  e— 

11 

'-^  —  ' 

—  S  ^ 

•^ 

IMI  N 

§139.  As  a  last  example  we  give  a  musical  sentence 
that  will  illustrate  the  possibilities  of  free  modulation  into 
neighboring  keys. 


".- 


Double  Counterpoint 


201 


In  this  case,  to  show  tr-^  possibilities  of  combination  and 
to  secure  a  better  effe^-  on  the  pianoforte,  we  make  the 
inversion  by  changing  each  part  only  one  octave. 


Inversion 


§140.  The  student  should  now  write  double  counter- 
point sometimes  above,  sometimes  below,  to  the  following 
subjects,  modeling  his  style  in  accordance  with  the  pre- 
ceding examples. 


2. s*. i 


3. 


5. 


In  No.  5  it  is  suggested  that  the  counterpoint  be  written 
in  the  rhythm  of  two  eighth  notes  against  each  quarter 
note  of  the  subject. 


In  No.  6  let  the  counterpoint  move  in  the  rhythm  of  four 
sixteenths  against  each  quarter  note  of  the  subject. 

| §14 1.  In  connection  with  the  above  exercises  the  stu- 
dent should  also  write  short  sentences  in  two-part  double 
counterpoint,  in  which  he  himself  invents  both  subject  and 
counterpoint.  This  work  will  prove  to  be  interesting  and 


204 


Tonal  Counterpoint 


most  stimulating  to  his  ingenuity.  As  soon  as  a  reason- 
able degree  of  facility  has  been  acquired,  he  should  begin 
to  analyze  the  two-part  inventions  of  J.  S.  Bach.*  When 
the  simple  principles  of  form  and  style  have  been  mas- 
tered, he  should  begin  to  compose  short  inventions 
in  two  voices.  Attempts  in  this  field  are  always  most 
delightful  to  the  musician  with  a  natural  enthusiasm  for 
creative  work,  and  often  short  pianoforte  pieces  of  per- 
manent artistic  worth  are  the  result. 

§142.  Let  us  now  analyze  one  of  these  two-voiced 
inventions.  They  are  all  written  in  what  is  known  as  two- 
part  or  binary  form,  and  we  see  in  them  the  same  simple 
design  that  runs  through  all  early  instrumental  composi- 
tions,—  prelude,  allemande,  courante,  gavotte,  sarabande, 
etc.f  In  the  first  invention,  for  example,  we  find  a  short, 
melodious  phrase  given  out  in  the  upper  voice : 


This  theme  which,  as  we  shall  see,  is  the  foundation  of 
the  entire  composition,  is  at  once  repeated  in  the  lower 
voice,  while  the  upper  voice  continues  with  an  appropriate, 
contrasting  counter  melody;  that  is, 


§143.  The  counter  melody,  however,  may  not  be  written 
in  free  style,  but  is  to  be  planned  with  reference  to  inversion ; 
that  is,  so  that  it  may  be  used  either  above  or  below  the  chief 
theme.  It  is  just  here  that  double  counterpoint  plays  a 
definite  part  in  the  structure,  for  when  we  come  to  what 
is  known  as  the  second  part  of  the  invention,  we  always 
find  the  theme  and  the  counter  subject  in  an  inverted 
relationship.  After  the  tonality  has  been  established  in 

*  The  instructive  edition  of  Busoni,  published  by  Breitkopf  and  Haertel,  is  espe- 
cially recommended.  Compare  also  that  of  Bockelman. 

t  As  this  is  not  a  book  on  Musical  Form  the  student  is  referred,  for  detailed  infor- 
mation, to  those  most  useful  treatises  of  Prout's,  —  "  Musical  Form  "  and  "  Applied 
Forms." 


Double  Counterpoint 


205 


the  opening  measures  modulation  always  begins,  and  it 
is  generally  along  the  simplest  and  most  natural  lines; 
that  is,  if  the  invention  is  in  the  major  mode,  the  first  mod- 
ulation is  to  the  dominant ;  *  if  in  the  minor  mode  either 
to  the  relative  major  or  to  the  dominant  minor.  For  exam- 
ple, in  the  invention  in  C  major  which  we  are  analyzing, 
when  the  key  of  G  major  (the  dominant)  has  been  reached, 
we  find  the  themes  presented  in  the  following  inverted  rela- 
tionship, that  is,  the  theme  is  given  out  in  the  lower  voice, 
is  repeated  above,  and  the  counter  subject  appears  in  the 
lo-iccr  voice  instead  of  the  upper: 


The  last  part  of  an  invention  is  rather  free,  and  no  fixed 
rules  can  be  given  for  its  construction.  In  the  return  to  the 
original  tonic  key,  passing  modulations  are  always  intro- 
duced (into  related  keys),  —  that  is,  into  the  three  relative 
minors  and  into  the  subdominant.  The  structure  is 
always  so  carefully  designed  that  the  second  part,  as  a 
whole,  may  be  subdivided  into  two  more  parts.  Thus 
the  composition  in  the  main  exhibits  strong  tendencies, 
as  far  as  key  relationship  is  concerned,  toward  three-part 
form;  that  is, 


First  Part 


Third  Part 


Tonic  (major)  Dominant  Return  to  original  key 

(minor)  ,,  (minor) 

or  relative  major;  related  keys  (coda) 

During  the  modulatory  passage  at  the  end  of  Part  I  and 
throughout  Part  III,  the  student  should  strive  to  avoid 
all  aimless  wandering  about.  To  this  end  let  him  employ 
sequences  and  frequent  simple  imitations  between  the 
voices.  He  should  play  and  carefully  analyze  inventions 
Nos.  i,  8,  10,  4,  3,  2  and  5  (to  begin  with  —  the  freer  ones 
later).  The  only  way  to  acquire  a  good  style  in  this  form 
of  writing  is  to  observe  the  varied  devices  with  which  Bach 

*  Rarely  to  the  relative  minor;  compare,  however,  the  fifth  invention. 


206 


Tonal  Counterpoint 


always  holds  the  interest  of  the  hearer.  In  the  first 
invention,  for  example,  after  the  related  key  of  A  minor 
has  been  reached  in  the  fifteenth  measure,  Bach  takes  the 
original  motive  and  transforms  it  from 


that  is,  the  same  phrase  in  contrary  motion,  and 
then,  after  playing  about  with  simple  sequences  in  the 
keys  of  D  minor  and  F  major,  he  works  to  a  strong  close  in 
C  major  with  the  motive  in  its  original  form.  We  now 
give  a  few  themes  for  inventions  which  should  be  worked 
out  in  accordance  with  the  model  from  Bach  analyzed 
above.  As  soon  as  the  form  is  clearly  understood  the  stu- 
dent should  himself  invent  some  motives  suitable  for 
treatment. 

Allegro  moderate 
1. 


Allegro  non  troppo 

2. 


Andantino 


Double  Counterpoint 


207 


Allegro  con  spirito 


m 


Tempo  modera 

||\4  1 

to 

F= 

i   nrji 

~^~  —  i  rpi. 

If  d  j  «  1 

It  must  be  clearly  understood  that  in  these  exercises  the 
counterpoint  is  to  be  written  with  reference  to  subsequent 
inversion.  For  instance,  in  No.  i,  the  first  definite  modu- 
lation will  probably  be  to  the  dominant,  and  the  second 
part  would  begin  thus: 


It  is  evident  that  this  is  the  same  counterpoint  below  (with 
the  exception  of  one  note,  to  avoid  an  empty  fourth  at  the 
beginning  of  the  measure)  which  was  used  at  the  begin- 
ning above  the  subject.  In  working  out  No.  3  it  is  sug- 
gested that  the  first  modulation  be  made  to  the  dominant 


208 


Tonal  Counterpoint 


minor  instead  of  the  relative  major, 
the  two  voices  invert  as  follows: 


This  would  make 


§144.  For  the  student  who  has  thoroughly  grasped  the 
principles  of  double  counterpoint  in  two  voices,  triple  and 
quadruple  counterpoint  will  present  but  few  additional 
difficulties.  By  these  terms  we  mean  three  or  four  inde- 
pendent melodies,  so  planned  that  each  one  is  capable  of 
being  the  highest  part,  the  lowest  part,  or  one  of  the  inner 
voices.  In  all  the  combinations  the  harmony  so  formed 
must  be  correct.  Three  independent  melodies  written  in 
double  counterpoint  are  obviously  capable  of  six  different 
combinations.  It  generally  happens  that  certain  of  these 
combinations  are  more  effective  than  others,  and  it  is  sel- 
dom necessary  or  advisable  to  use  all  six  positions.  Each 
one  of  the  three  voices,  however,  should  be  introduced 
once  in  the  bass.  This  test  will  most  readily  disclose 
faults,  for  the  only  essential  way  in  which  triple  counter- 
point differs  from  ordinary  double  counterpoint  is  in  the 
treatment,  in  any  one  of  the  upper  voices,  of  the  fifth  of  a 
chord  (either  a  triad  or  a  chord  of  the  seventh)  with  refer- 
ence to  its  subsequent  appearance  in  the  bass.  Unless 
very  carefully  handled,  it  will  make  bad  six-four  and  three- 
four  chords.  No  definite  rules  can  be  laid  down  in  regard 
to  this  point  without  hampering  the  student  more  than 
helping  him.  He  must  simply  study  good  models,  prac- 
tise under  supervision,  and  gradually  cultivate  a  reliable 
judgment.  In  general,  it  is  better  in  the  upper  voice  to 
use  the  fifth  sparingly,  especially  in  the  secondary  triads 
of  the  key  (n,  in,  vi),  as  the  second  inversions  of  these  weak 
chords  are  seldom  satisfactory.  When  the  fifth  is  intro- 
duced, it  should  almost  invariably  be  by  step  and  not  by 
leap. 

§145.  It  is  evident  that  consecutive  chords  of  the  sixth 
are  not  available  in  triple  counterpoint. 


IE 


6     6 


Double  Counterpoint 


:og 


as  in  some  of  the  inversions  parallel  fifths  will  necessarily 
be  the  result. 

§146.  Four  independent  melodies  written  in  double 
counterpoint  will  allow  twenty-four  possible  combina- 
tions. It  is  needless  to  say  that  all  these  positions  are  not 
used  in  a  single  composition.  Composers  select  only  those 
which  seem  most  effective  and  interesting. 

§147.  A  few  original  exercises  are  now  given  for  the 
student  to  work  out.  He  will  seldom  have  occasion  to 
use  triple  and  quadruple  counterpoint  except  in  advanced 
fugal  and  symphonic  writing.  By  that  time,  wherever 
double  counterpoint  would  increase  the  organic  structure 
of  a  composition  or  add  to  the  vital  interest,  there  will  be 
little  trouble  in  using  it  properly.  Double  counterpoint, 
introduced  merely  for  its  own  sake,  always  sounds  labored 
and  pedantic.  For  the  present,  the  student's  time  will 
be  much  better  employed  in  analyzing  and  copying  well- 
selected  examples  of  double  counterpoint  from  the  works 
of  great  contrapuntal  writers:  Bach,  Handel,  Mozart,  etc. 
In  the  fourth  fugue  of  the  first  book  of  "  The  Well-Tem- 
pered Clavichord,"  we  find  three  melodies  treated  in  double 
counterpoint. 


0  tf  "      /      J  J  * 

«l  J  J-^-^J  J  J 

3 

*J'Ysr  " 

ttJ            V     = 

etc. 

if  M,' 

[     jf  

i    J   J    1                    — 

s        «* 

=£rr 

$Y     f 

ffffrr^fF 

efo 

1  B_  

J  r  '  ' 

Mill: 

210 


Tonal  Counterpoint 


The  six  possible  combinations  of  these  voices  are  all 
satisfactory,  and  are  actually  used  in  the  course  of  the 
fugue,  though  sometimes  in  related  keys.  It  simplifies 
matters,  however,  to  retain  one  key,  and  it  will  be  well  for 
the  student  to  complete  (b)  and  (c)  and  to  write  out  the 
other  three  combinations. 

§148.  Other  beautiful  and  instructive  examples  of  triple 
counterpoint  from  the  forty-eight  Preludes  and  Fugues  are 
the  following:  Prelude  in  A  major,  No.  19,  Book  i  (four 
of  the  six  possible  combinations  are  used) ;  Fugue  in  C# 
major,  No.  3,  Book  i.  The  Fugue  in  Bb  major,  No.  21, 
Book  i,  with  the  exception  of  two  episodes,  is  written 
throughout  in  triple  counterpoint,  and  will  furnish  a  most 
stimulating  model  for  the  student.  The  three-part  Fugue 
in  F#  major,  No.  13  of  Book  2,  is  particularly  valuable  as 
an  illustration  from  the  fact  that  all  six  possible  inversions 
are  used.  We  give  the  first  appearance  of  the  three  con- 
trasted melodies,  written  out  in  open  score,  that  the  mel- 
odic line  of  each  part  may  be  more  easily  followed.  We 
strongly  advise  the  student  to  adopt  this  method  in 
analyzing  the  various  examples  in  triple  and  quadruple 
counterpoint.  Not  only  do  the  individual  melodies  stand 
out  more  clearly,  but  most  valuable  practice  is  afforded  the 
eye  with  reference  to  subsequent  reading  of  orchestral 
scores.  In  this  a  wide  and  accurate  range  of  vision  is 
absolutely  indispensable. 


Let  the  student  write  out  the  other  three  positions  for 
himself,  beginning  at  measure  forty-four.  In  the  follow- 
ing example  taken  from  a  chorus  in  Handel's  opera,  "  Her- 
cules," 


Double  Counterpoint 


21  T 


.1  lodcrato 


all  six  positions  are  effective  and  should  be  written  out, 
though  in  the  actual  score  the  composer  uses  but  four. 
As  a  last  illustration  let  the  student  look  up  the  magnifi- 
cent examples  of  triple  counterpoint  found  in  Bach's  well- 
known  organ  Fugue  in  G  minor. 


All  six  positions  of  these  wonderfully  contrasted  voices 
are  used  in  the  course  of  the  fugue. 

EXERCISES 


jrjpH* 

A  ^- 

^11^ 

_dfc 

• 

IF* 

B-4  

^ 

etc 

BE 

**F* 

y4=L 

s 

\  n 

i  i  i 

±^ 

y^y 

While  he  is  completing  voices  A  and  B,  let  the  student 
bear  in  mind  their  subsequent  use  as  a  bass.  They  should, 
therefore,  be  kept  simple.  All  six  inversions  are  satis- 
factory. 


212 


Tonal  Counterpoint 


HE 

MJ 

s 

1 

P 

id 

II  _    Jj 

i 

tr 
P 

etc. 

B 

^ 

I 

"      f    1 

8r 


III.  «           i 

5' 

trrrti  

»»rffr 

ffp' 

s~ 

s 

!  1 

a  —  L  1 

rrj  *  i 

0  • 

In  working  out  the  above  exercises  let  the  student  bear 
in  mind  that  it  frequently  happens  that  certain  positions 
of  triple  counterpoint  sound  more  satisfactory  than  others. 


Double  Counterpoint 


21 


In  regard  to  the  fifth,  of  course  it  is  not  to  be  avoided  alto- 
gether; the  chief  point  is  to  introduce  it  with  thoroughly 
good  results. 

§149.  When  four  voices  are  so  written  that  any  one  may 
be  used  in  any  position  we  have  quadruple  counterpoint. 
If  all  the  inversions  are  made,  there  are  twenty -four  pos- 
sible combinations.  It  is  needless  to  say  that  out  of  this 
number  only  the  most  interesting  ones  are  selected.  For 
this  kind  of  counterpoint  no  new  rules  are  necessary;  the 
fifth  of  a  chord  always  needs  special  care,  and  the  student 
should  endeavor  to  make  each  voice  distinct  in  character 
from  the  others.  It  is  always  of  good  effect  to  have  the 
voices  enter  in  succession,  and  it  is  never  necessary  to  have 
all  the  voices  moving  at  the  same  time.  Rests  properly 
introduced  afford  great  contrast  and  variety.  As  quad- 
ruple counterpoint  from  its  complexity  is  much  less  com- 
mon than  double  or  triple,  a  few  examples  and  exercises 
will  suffice.  One  of  the  most  comprehensive  and  inter- 
esting illustrations  may  be  found  in  the  four-voiced  Fugue 
in  E  major  (No.  9  of  the  second  book  of  the  "  Forty-Eight "), 
beginning  at  the  sixteenth  measure.  The  passage  has 
been  written  out  in  open  score,  as  if  for  string  quartet,  in 
order  that  the  melodic  course  of  each  voice  may  be  more 
readily  followed. 

jJL  A 


t 


^ 


£ft 


D 

^m 


ae 


214 


Tonal  Counterpoint 


In  the  Fugue  in  F  minor  (No.  12  of  the  first  book)  there 
may  also  be  found  an  instructive  passage  in  quadruple 
counterpoint  at  the  thirteenth  measure.  The  inversion 
takes  place  at  measure  twenty-seven.  Lastly,  a  most  won- 
derful example  (both  in  its  complexity  and  yet  in  its  per- 
fect freedom)  may  be  found  in  the  finale  of  Haydn's 
Quartet  in  C  major,  Op.  20,  No.  2,  which  is  a  fugue  on  four 
subjects.  The  student  can  hardly  do  better  than  to  look 
up  this  movement  and  copy  out  the  various  positions. 

§150.  Complete  the  following  exercises  in  quadruple 
counterpoint,  and  write  out  at  least  three  inversions;  that 
is,  test  the  voices  by  using  each  one  in  the  bass. 


I 


H    A 


^ 


B 


8  fr  - 


,,l2L-4^  .  —  , 

fffrri 

1 

W)     4  *  J  *  J 

iVrt 
-*  —  i  i  ^ 

s 

+   J  0  m 

U  —  L4  1 

*^ 

~*~m 

^tt 

U 

§151.  For  a  marvelous  example  of  quintuple  counterpoint 
let  the  student  study  the  finale  to  Mozart's  "Jupiter" 
Symphony,  in  which  five  separate  subjects  are  combined  in 
all  varieties  of  inversion  and  combination. 


CHAPTER  X 


Imitative  Counterpoint 

§152.  The  student  should  now  work  out  some  exercises 
in  which  the  principle  of  imitation  is  systematically  intro- 
duced. Imitation  consists  in  the  repetition  of  the  same 
melodic  figure  in  various  voices  on  different  scale  degrees 
and  oftentimes  in  different  keys.  Every  one  is  aware  of 
the  great  coherency  and  interest  imparted  to  music  by 
imitation  and  of  its  frequency  in  the  works  of  all  good 
composers.  In  all  elaborate  polyphonic  writing  (such  as 
canon  and  fugue)  imitation  plays  an  important  and  essen- 
tial part,  but  even  in  the  freest  and  lightest  forms  of  com- 
position, its  subtle  use  is  far  more  frequent  than  is  generally 
supposed.  The  subject  is  so  broad  and  indefinable  that 
no  fixed  rules  can  be  given  for  the  use  of  imitation.  Some 
examples  are  cited  to  show  the  general  style,  and  then  sev- 
eral exercises  should  be  worked  out. 


J    J 


SCHUMANN.    Song 


aM 


SCHUMANN.    Jugend  Album 


etc. 


SCHUMANN.     Arabeske 


2l6 


Tonal  Counterpoint 


§153.  See  also  the  Sixth  and  Seventh  Novelettes,  the 
first  intermezzo  of  the  Third  Romance,  Op.  28,  and  the 
last  of  the  Fantasie-stiicke,  Op.  1 2 ,  for  charming  examples  of 
free  imitation.  Schumann's  compositions,  in  fact,  abound  in 
masterly  and  artistic  uses  of  imitation,  and  the  student  is 
earnestly  advised  to  look  up  examples  for  himself.  A 
beautiful  example  in  vocal  style  may  be  found  in  the  chorus 
of  "Houris"  in  the  "Paradise  and  Peri"  of  the  same 
composer.  The  older  contrapuntists  devoted  much  time 
and  skill  to  imitation  (so  much  so  that  at  tim.es  their  work 
sounds  labored  and  artificial);  the  compositions  of  Bach, 
however,  are  an  inexhaustible  mine  of  instructive  exam- 
ples for  the  student. 


"  Well-Tempered  Clavichord,"  Book  i,  Prelude  IV 


1  Well-Tempered  Clavichord,"  Book  i.  Prelude  Vil 


§154.  See  also  Preludes  Nos.  9  and  23  of  the  first  book 
of  the  "Forty-Eight,"  and  Prelude  No.  7  of  the  second 
book,  for  interesting  examples  of  free'  imitation.  Through- 
out Beethoven's  sonatas  there  are  plentiful  passages  to 
illustrate  this  principle.  In  the  finale  of  Op.  26  the  stu- 
dent may  see  the  close  relationship  between  double  coun- 
terpoint and  imitation;  in  fact,  they  are  very  often  found 
together. 

§155.  That  the  imitation  need  not  be  literal  nor  too  exact 
in  order  to  produce  the  delightful  effect  of  answering  voices 
so  noticeable  in  modern  composition  is  shown  by  the 
following  striking  passages: 


Imitative  Counterpoint 


217 


Andante 


TSCHAIKOWSKI.      Concerto,  Op.  23 


J 


FfT 


marcato 


s 


m 


^n  Joj  j 


j  jo*  4  r  ^r~nj 


y= 


*    ig~^_^ 
f  -T^=r 


BRAHMS.     Vocal  Quartet,  Op.  64 


LEES 


218 


Tonal  Counterpoint 
EXERCISES 


I 

\*TJ 


33 


f 


§156.  With  each  of  the  above  motives  let  the  student 
compose  a  musical  sentence  of  twelve  or  of  sixteen  meas- 
ures.* Modulation  into  related  keys  should  be  freely  used. 
It  is  also  very  interesting  and  beneficial  to  improvise  at 
the  pianoforte  or  organ  short  preludes  in  which  some 
motive  is  introduced  and  developed  in  the  various  voices. 
Two  models  of  style  are  given  for  the  organ. 


§157.  The  following  prelude  from  one  of  Tschaikowski's 
songs  (Op.  28,  No.  3)  will  furnish  a  beautiful  motive  for 
development  in  free  pianoforte  style: 

*  The  working  out  should  be  in  open  score. 


Imitative  Counterpoint 


219 


§158.  Some  longer  periodic  melodies  should  now  be 
treated  with  imitative  counterpoint.  In  each  of  the  fol- 
lowing exercises,  for  instance,  continue  to  introduce  in  the 
different  voices,  as  often  as  it  will  appear  naturally,  the 
short  melodic  phrase  with  which  the  counterpoint  begins. 

1. 


*£ 


i 


The  same  melody  in  the  alto  with  an  ascending  phrase 
for  the  figure. 


ii 


220 


Tonal  Counterpoint 


Good  practice  is   also  afforded  by  the  treatment  of  the 
same  bass  with  a  descending  figure. 


§159.  For  a  beautiful  example  of  the  treatment  of  a 
choral  melody  with  imitations,  see  Bach's  version  of  the 
melody  "Vom  Himmel  hoch  da  komm  Ich  her."  * 


C.F. 


*  This  is  to  be   found  in   th^  Appendix  to  the  eleventh   volume  of  the  Bach- 
Gesellschaft  edition. 


Imitative  Counterpoint  221 

Here  the  imitating  voices  which  accompany  the  soprano 
are  derived  (by  diminution)  in  the  most  ingenious  way 
from  the  melody  itself.  The  whole  choral  will  repay  care- 
ful analysis. 

§160.  Henceforth  in  all  his  work,  especially  that  for 
voices  or  for  strings,  the  student  should  be  on  the  watch 
to  introduce  imitative  phrases,  not  so  often,  to  be  sure, 
as  in  the  above  exercises,  where  the  repetition,  to  secure 
facility,  was  somewhat  mechanical,  but  wherever  the 
organic  structure  of  the  composition  may  be  strengthened. 
Only  a  mature  artistic  judgment  can  decide  just  where  and 
just  how  often  imitation  may  be  introduced  with  happy 
and  convincing  effect.  Meanwhile  the  cultivation  of  this 
tendency  is  a  most  effective  cure  for  a  diffuse  and  wan- 
dering style. 


CHAPTER    XI 
Pianoforte  Writing 

§161.  We  shall  now  give  some  melodies  which  are  to  be 
harmonized  with  especial  reference  to  their  effectiveness 
upon  the  pianoforte.  First,  however,  something  must  be 
said  of  the  distinction  between  homophonic  and  polyphonic 
style,  for  the  student  has  doubtless  noticed  in  compositions 
for  the  pianoforte  how  seldom  all  the  parts  are  of  equal 
importance,  and  how  free  the  writing  is  in  regard  to  the 
number  of  voices,  range,  etc. 

§162.  In  poly  phonic  music,  as  we  have  seen,  all  the  voices 
are  held  to  be  of  equal  melodic  importance  and  are  treated 
accordingly,  whereas  the  essential  of  homophonic  music 
is  that  there  shall  be  one  chief  melody  (either  in  an  upper, 
a  middle,  or  a  lower  voice,  as  the  case  may  be),  while 
the  other  parts  are  kept  frankly  subordinate  and  merely 
furnish  a  harmonic  background,  or  accompaniment.  In 
most  music,  however,  of  any  worth,  this  accompaniment 
is  so  contrived  that  it  has  some  independent  rhythmi- 
cal interest  which  is  secured  by  the  continued  use  of 
the  same  accompaniment  figure, —  often  some  charac- 
teristic arpeggio  or  group  of  iterated  chords.  In  all 
modern  writing  for  the  pianoforte,  beginning  with  Bee- 
thoven, this  homophonic  style  predominates,  although  in 
compositions  of  large  extent  we  often  find  both  styles. 
Composers  themselves  differ,  in  that  some  are  more  contra- 
puntal in  their  tendencies  than  others.  Chopin,  for  exam- 
ple, writes  in  many  instances  in  the  style  of  an  idealized 
modernized  Bach.  Schumann  is  very  polyphonic  in  much 
of  his  pianoforte  music.  The  chief  essential  in  learning 
to  write  effectively  for  the  pianoforte  is  to  free  ourselves 
from  some  of  the  very  tendencies  which  are  so  important 
in  compositions  for  voices  or  for  strings,  —  that  is,  a  fixed 
number  of  parts  and  a  definite,  melodic  individuality  for 
each  voice.  The  keys  of  a  pianoforte  are  not  personalities 
like  the  singers  in  a  chorus  or  the  players  in  a  quartet  or 
orchestra,  whose  interest  has  to  be  kept  up  by  the  com- 
poser. In  writing  for  the  pianoforte  it  is  entirely  a  matter 
of  artistic  judgment  whether  the  number  of  parts  shall  be 
two  or  ten.  In  fact,  some  of  the  most  beautiful  composi- 
tions known  are  largely  in  two-part  writing,  with  an  occa- 


Free  Writing  for  Pianoforte  22^ 

sional  appearance  of  fuller  harmony  where  effects  of  forte 
or  of  sforzando  are  required.  This  is  equally  true  of  the 
works  of  Beethoven,  of  Schumann,  or  of  Chopin  —  three 
great  masters  of  pianoforte  style.  In  this  style  of  writing, 
thinness  of  harmony  is  avoided  by  a  frequent  use  of  broken 
chords  and  arpeggios,  and  sonority  of  effect  is  gained  by 
a  free  use  of  the  damper  pedal.  These  points  are  clearly 
shown  in  the  following  illustrations: 


BEETHOVEN.    Sonata  Pathdtique,  Rondo 


Allegro . 


Allegro  con  brio 


BEETHOVEN.    Sonata,  Op.  22 


22  A 
Andantino 


Tonal  Counterpoint 

SCHUMANN.    Little  Study,  Op. 


etc. 


Andante  con  ntoto 


i 


1 


SCHUMANN.    ?th  Novellette,  Trio 


J    J     J 


sat 


Pedal  sempre 


etc. 


Free  Writing  for  Pianoforte 


22  • 


CHOPIN.     Funeral  March 


CHOPIN.    Op.  22,  Polonaise 


§163.  In  these  beautiful  and  very  instructive  examples, 
observe  how  distinctly  the  cantabile  melody  stands  out, 
while  at  the  same  time  the  harmonic  basis  outlined  by  the 
accompaniment  figures  is  uniformly  rich  and  satisfying. 
In  the  selections  from  Schumann  and  Chopin  observe  the 
wide  extent  of  the  arpeggios  (so  characteristic  of  the  modern 
school)  in  contrast  with  the  grouping  used  by  Beethoven 
and  the  older  classic  masters,  who  generally  kept  arpeggios 
within  the  octave. 

§164.  The  accompaniment  to  a  melody  may  often  con- 
sist of  a  series  of  iterated  chords.  When  this  form  of 
accompaniment  is  used  the  melody  is  generally  character- 
istic enough  to  justify  the  subordination  of  the  harmonic 
background.  But  even  in  the  chords  themselves,  when 
the  student  applies  this  treatment  to  his  own  work,  a  cer- 
tain distinction  should  be  sought,  for  nothing  is  more 
monotonous  than  the  endless  repetition  of  a  few  trite 
harmonies. 


226 


Tonal  Counterpoint 


Allegro 


MOZART.     Sonata  in  A  minor 


Allegro 


BEETHOVEN.    Sonata,  Op.  14,  No.  i 


Allegro 


SCHUMANN.    Jugend  Album,  No.  10 


Largo 


CHOPIN.     Preludes,  No.  4 


§165.  Unfortunately,  it  is  impossible  to  lay  down  any 
fixed  rules  to  teach  the  student  how  to  write  effectively  for 
the  pianoforte.  His  best  method  of  work  is  to  harmonize 
certain  melodies  in  pianoforte  style,  as  soon  as  possible  to 
try  his  own  hand  at  short  original  pieces,  and  to  follow  the 
criticisms  and  suggestions  of  his  teacher.  Above  all,  let  him 
play  and  analyze  the  standard  works  in  pianoforte  litera- 
ture, especially  the  compositions  of  Chopin,  Schumann, 
Heller,  and  Liszt.  The  pianoforte,  as  an  instrument,  has 
great  advantages.  Its  compass  is  very  large,  it  is  well 


Free  Writing  for  Pianoforte 


227 


suited  to  the  homophonic,  and  also  (with  modifications)  to 
the  polyphonic  style,  the  uniformity  of  tone  quality  through- 
out its  compass  is  of  great  practical  advantage,*  and  music 
written  for  any  other  instrument  can  be  suitably  tran- 
scribed for  it.  On  the  other  hand,  it  has  certain  deficien- 
cies which  must  be  carefully  considered;  for  example, 
sounds  cannot  be  sustained  with  uniform  strength  as 
with  the  voice,  the  organ  or  violin,  or  with  most  orchestral 
instruments,  and  of  course  a  crescendo  on  a  held  tone  is 
absolutely  impossible;  —  whatever  sustaining  .power  the 
instrument  possesses  is  far  greater  in  the  lower  and  middle 
registers  than  in  the  higher  compass.  From  these  inherent 
characteristics  certain  deductions  can  be  made  which 
should  prove  helpful. 

§166.  First:  In  general  (especially  in  early  attempts),  let 
the  style  be  light.  Two-  and  three-part  writing  is  always 
effective  on  the  pianoforte,  as  the  student  may  see  for 
himself  from  the  numerous  examples  in  the  works 
of  Bach,  Schumann,  Chopin  and  Mendelssohn;  well- 
grouped  arpeggios,  sustained  by  the  pedal,  may  always  be 
counted  upon  for  sufficient  sonority. 

Second :  Avoid  thick  and  muddy  chords.  In  the  writings 
of  Haydn,  Beethoven  and  their  contemporaries,  we  often 
find  chords  like  the  following: 


Adagio 


HAYDN".    Sonata  in 


BEETHOVEN.    Op.  3,  No.  i 


r 


BEETHOVEN'.    Op.  10,  No.  3 


BEETHOVEN.    Op.  7 


*  In  writing  for  voices  or  for  orchestral  instruments,  great  attention  has  to  be 
paid  to  the  different  registers,  —  chest  tone,  head  tone,  or  grave,  medium  and  acute 
register  of  clarinet,  flute,  etc.,  and  often  the  composer  is  seriously  hampered  by 
mechanical  difficulties. 


228 


Tonal  Coin     >-point 


§167.'  The  reason  is  not  far  t  eek.  The  instruments  of 
the  latter  part  of  the  eighteenth  tury  and  the  early  part 
of  the  nineteenth  had  a  rather  ligi  hin  tone,  and  compos- 
ers, in  their  endeavors  to  secure  rich  .  md  brilliancy ,  often 
wrote  chords  which  upon  our  more  •  avily  strung  and 
richer  toned  pianos  sound  thick  and  coarse,  and  in  which 
the  sonority  is  deadened  rather  than  'n creased.  In  gen- 
eral, chords  should  be  so  grouped  th,"  there  are  spaces 
between  the  factors  in  which  the  harmonics  may  vibrate; 
if  everything  is  filled  in,  more  noise  is  made,  but  not  more 
clear,  ringing,  musical  sound.  In  this  connection  avoid 
placing  the  third  or  doubling  the  third  in  the  lower  register. 
Thirds  in  close  position  do  not  sound  well  in  that  part  of 
the  instrument.  For  instance,  such  doubling  of  thirds 
and  of  leading  tones  as  may  be  found  above  in  example  (a) 
is  seldom  advisable,  and  the  low  thirds  in  example  (6)  and 
(c)  have  a  rather  gruff  effect.  In  example  (d)  a  modern 
composer  would  have  undoubtedly  resolved  the  last  beat 
of  the  measure  in  this  position, — 


p=^ 


with  a  great  gain  in  real  sonority.  This  rule  about  thirds 
is  applicable  also  to  arpeggios.  In  older  compositions 
we  find  figures  like  this : 


but  since  the  time  of  Von  Weber  and  Chopin,  who  were  the 
pioneers  in  using  widely  dispersed  positions,  it  is  far  more 
common  and  better  to  find  the  third  treated  as  a  tenth  and 
to  employ  a  more  open  grouping;  that  is, 


Of  course  care  must  be  taken  not  to  write  arpeggios  actually 
beyond  the  compass  of  the  human  hand.     Groups  like  the 


Free  Write  -y,  for  Pianoforte 


229 


following  are  entirely  ir      jssible  on  the  piano  at  a  high 
rate  of  speed, 


Allegro 


and  are  really  violin  figures.  Only  a  mature  judgment 
and  an  intimate  knowledge  of  pianoforte  technique  will 
enable  the  student  to  decide  in  every  case  just  what  is 
practicable,  —  klaviermassig,  as  the  German  term  is. 
Hence  at  the  outset  let  the  style  be  simple  and  direct. 
Avoid  chords  which  consist  of  huge  handfuls  of  notes  — 
especially  when  they  imply  rapid  change  of  position  — 
and  also  fantastic  groupings  of  arpeggios. 

§168.  Third:  When,  for  variety,  the  polyphonic  style  is 
used,  and  this  is  often  the  case,  avoid  many  complicated,  in- 
dependent parts.  Two-  and  three-part  writing  will  generally 
suffice;  each  additional  voice  not  only  increases  the  tech- 
nical difficulty  for  the  player,  but  renders  the  music  less 
easy  to  be  followed  clearly  by  the  hearer.  In  all  two-part 
writing  care  should  be  taken  not  to  have  the  separate 
voices  too  far  apart;  when  they  are  so  separated  there  is 
an  effect  of  thinness  and  emptiness  which,  in  general, 
is  not  desirable.  A  cantabile  melody  should  practically 
always  be  given  to  the  medium  part  of  the  instrument, 
as  there  the  singing  power  is  strongest. 

§  169.  We  now  take  a  simple  melody  by  Mozart,  and  pro- 
ceed to  harmonize  it  in  pianoforte  style.  It  will  be  ad- 
visable for  the  student  to  try  his  own  hand  at  this  melody 
in  accordance  with  the  suggestions  given  above,  and  then 
compare  it  with  the  version  which  is  submitted  as  an  illus- 
tration of  the  main  points  in  pianoforte  style,  but  not  as 
the  only  treatment  of  which  the  theme  is  capable. 


Tempo  di  minuetto 


Tonal  Counterpoint 


I 


si 


"if 


J 


Free  Writing  for  Pianoforte 


211 


The  following  points  in  the  above  version  are  to  be  care- 
fully noticed  by  the  student :  The  light  style  of  the  open- 
ing measures,  thoroughly  in  keeping  with  the  simplicity 
of  the  melody.  Often  the  theme  stands  out  better  if  it  is 
entirely  without  accompaniment  for  a  few  notes,  as  in 
measures  three,  five,  etc.  Observe  the  freedom  from  a 
fixed  number  of  parts;  sometimes  the  chords  have  two 
parts,  sometimes  six.  In  the  last  measures  animation  is 
gained  by  changing  the  eighth-note  motion  to  triplets.  Of 
course  at  (a)  and  (b)  sonority  is  gained  by  the  sustaining 
pedal. 

§170.  A  set  of  melodies  is  now  given  which  the  student 
is  to  treat  himself.  Strive  for  variety  and  beauty  in  the 
accompaniment.  Mendelssohn's  "Songs  without  Words" 
furnish  an  endless  variety  of  accompaniment  figures  for 
lyric  melodies,  and  they  may  be  studied  with  great  profit 
in  connection  with  the  original  work. 


Andante  cantabile 


MOZART 


Tonal  Counterpoint 


-  f 


The  next  melody  gives  opportunity  to  use  an  accompani- 
ment of  iterated  chords,  which  may  be  interchanged  in 
places  with  other  figures. 


2.      Presto  agitato 


MEXDELSSOHN 


M*  J-J 

W)  *       yj»i 


m 


7\  J   '+  J- 


cre 


Ff^ 


ft 

i     r 


Free  Writing  for  Pianoforte 


2.33 


3.     Adagio  cspressivo 


BEETHOVEN 


At  (a)  observe  the  slight  change  in  the  figure  to  avoid  the 
doubling  of  the  leading  tone  B.  Such  attention  to  detail 
conduces  to  clearness  of  style. 


Andante  vivace 


BEETHOVEN 


r 


f£ 


f^f 


Tonal  Counterpoint 


7.     Tempo  di  Marcui 


BOIELDIEN 


Free  Writing  for  Pianoforte 


$171.  In  connection  with  these  exercises  the  student  is 
strongly  urged  to  begin  work  entirely  original.  Short 
pieces  should  be  composed  for  the  piano  in  some  of  the 
dance  rhythms, —  minuet,  gavotte,  bourree,  scherzo,  —  and 
in  two-part  or  three-part  form.  A  constant  effort  should 
be  made  to  stimulate  the  inventive  faculties  and  to  enliven 
the  imagination.  Like  any  other  of  our  powers,  the  im- 
agination grows  strong  from  practice.  Nothing  will  teach 
the  student  so  much  about  pianoforte  style  as  to  try  his 
own  powers,  under  competent  supervision,  in  actual  orig- 
inal composition.  No  matter  how  latent  they  may  seem 
at  first,  they  will  surely  gain  strength  little  by  little. 
Facility  of  expression  oftentimes  reacts  most  favorably 
upon  the  ability  to  have  something  to  express. 


CHAPTER  XII 


Writing  for  String  Quartet 

§172.  We  now  give  a  set  of  melodies  of  varied  character, 
which  are  to  be  treated  with  special  reference  to  effective 
performance  upon  a  string  quartet.  Melodies  have  been 
selected  which  call  for  a  free  application  of  the  principles 
of  imitation  and  double  counterpoint  treated  in  the  fore- 
going chapters.  Likewise  the  homophonic  style  may  often 
be  applied  to  writing  for  strings,  though  a  little  more  care 
has  to  be  taken  to  make  the  subordinate  parts  interesting 
to  the  players  than  is  the  case  in  the  writing  of  an  accom- 
paniment for  a  keyed  instrument.  Above  all,  the  student 
is  expected  to  analyze  some  of  the  ever-beautiful  quartets 
of  Haydn,  Mozart,  Beethoven  and  Schubert.  In  these 
days  of  cheap  editions  of  the  classics,  there  is  no  reason 
for  not  owning  and  studying  thoroughly  certain  models 
of  style. 

The  following  are  especially  recommended:  from 
Haydn,  any  of  the  five  in  Op.  76;  from  Mozart,  of  the  set 
dedicated  to  Haydn,  those  in  C  major,  A  major  and  D 
major.  From  Beethoven,  the  three  in  Op.  18  are  good  ones 
with  which  to  begin.*  In  a  short,  practical  book,  it  is 
obviously  impossible  to  enter  upon  all  the  intricacies  of 
a  perfectly  free  string-style.  Perhaps  one  of  the  most 
important  points  is  the  freedom  with  which  the  inner 
voices  may  cross:  for  example, 


Sotto  voce 


MOZART.     Religious  March  from  "  Idomeneus" 


/rf  Violin 


CTl  J' 

{K  »(/  rJ      J*  at 


i 


^ 


^ 


^ 


2^  Violin 


ffiv^- 


^ 


. 

Viola 


Cello 


i 


*  These  may  all  be  procured  in  the  pocket  edition,  known  under  the  name  of 
"Payne's  Kleine  Partitur  Ausgabe." 

236 


Andante 


Writing  for  String  Quartet 

HAYDN.   Symphony  in  D 


Bassi 


tf  Violin 


R.  STRAUSS.    "  Till  Eulenspiegel 


§173.  Simple  as  these  passages  are,  they  illustrate  quite 
clearly  the  freedom  with  which  the  inner  voices  may  cross  in 
order  to  gain  variety  of  melodic  outline  and  to  give  certain 
important  chord  factors  to  just  the  most  sonorous  register 
of  a  given  instrument.  Any  one  who  has  ever  heard 
the  following  passages  from  the  symphonies  of  Schumann 
and  of  Brahms  will  remember  the  remarkable  richness  and 
sonority  gained  by  careful  grouping  of  the  chord  factors 
and  by  preserving  the  melodic  interest  in  each  voice. 


238 


Tonal  Counterpoint 

SCHUMANN,     zd  Symphony 


BRAHMS.     2d  Symphony 


p  espress. 


We  now  attempt  a  harmonization  for  string  quartet  of 
the  following  melody : 


Writing  for  String  Quartet 


As  elaborate  counterpoint  would  be  entirely  foreign  to  the 
simplicity  and  grace  of  the  melody,  it  is  better  to  treat  the 
three  lower  parts  as  an  accompaniment  and  to  use  chiefly 
the  homophonic  style.  The  harmonies  should  be  simple 
and  natural,  so  as  not  to  detract  from  the  individuality  of 
the  melody,  but  they  need  not  be  grouped  in  a  clumsy  or 
trite  fashion;  on  the  other  hand,  by  "  crossing,"  the  inner 
voices  may  be  made  quite  interesting. 

Allegretto 


mp 


Bpff? 


mp 


240 


Tonal  Con  nter.  point 


In  this  version  observe  the  crossing  of  the  second  violin  and 
the  viola  in  the  third  and  fourth  measures.  At  (a),  as  the 
outer  voices  are  separated  by  a  wide  range,  ' '  double  stop- 
ping" is  used  in  the  viola  for  two  chords.  In  this  way  the 
harmony  of  the  accompanying  voices  is  often  enriched. 
At  (6)  observe  how  the  suspension  saves  the  harmonic 
progression  from  being  commonplace. 

§174.  The  student  should  now  treat  the  following  melo- 
dies in  the  same  general  style  as  the  preceding  example. 
In  No.  3  the  writing  at  times  may  be  more  polyphonic. 
It  is  neither  necessary,  nor  in  fact  desirable,  to  keep  all  the 
parts  constantly  going.  Often  certain  of  the  instruments 
may  rest,  and  two-  and  three-part  writing  be  employed. 


Adagio 


HAYDN 


Andante 


SCHUBERT 


Writing  for  String  Quartet 


241 


Andante  grazioso 


HAVDX 


A  ndantino 


BEETHOVEX 


§175.  We  now  treat  a  melody  for  string  quartet  in  the 
polyphonic  style,  and  then  give  some  longer,  more  elabo- 
rate melodies  in  which  imitation,  double  counterpoint 
and  other  devices  may  be  freely  used.  The  student  should 
also  make  every  endeavor  to  have  his  exercises  and  com- 
positions performed.  More  is  to  be  learned  from  the  actual 
hearing  of  what  is  written  than  in  any  other  way. 


Poco  adagio 


HAYDX 


Tonal  Counterpoint 


In  this  version  observe  the  free  use  of  imitation  in  the  last 
seven  measures.  In  the  next  exercise  also  there  will  be 
frequent  opportunity  for  the  parts  to  answer  each  other. 


Andante  con  moto 


Writing  for  String  Quartet 


243 


•dim.    -  __ 

§176.  We  now  give  an  exercise  in  which  two  motives  are 
to  be  worked  out  simultaneously.  Imitative  phrases  of 
like  melodic  design  and  of  corresponding  rhythm  should 
be  freely  introduced. 


Adapted  from  Dubois 


2.    Andante 


244 


Tegipof. 


* 


*)     cresc.  ' 


^WW4£^ 


aim.  j>p 


§177.  The  melody  in  G  major  from  Haydn,  given  on 
p.  239,  may  also  be  treated  successfully  in  contrapuntal 
style,  that  is  with  a  flowing  obligate  in  one  of  the  inner 
voices.  We  work  out  a  few  measures  to  show  the  general 
style : 


3.    Allegretto 


«.     Andante  con  ntoto 


SCHUBERT 


Writing  for  String  Quartet 


245 


I    l"'«M||rJ.  J    IgEgEg* 
*  "-r-reso^--    P 


§178.  We  now  give  an  exercise  in  which  double  counter- 
point is  systematically  used  for  the  presentation  and 
development  of  two  themes. 


Moderato 


Adapted  from  DUBOIS 


in 


s^ 


tm 


m 


fa 


SP 


246 


i 


/•iPi   »Jft»(» 


E 

^fft 

-^ 

i*H=d 

^  - 

•s       i 

1  i"  '     ^'T  If" 

S±*=ttf 

s 


f»Lgi  BO  r-^- 


^ 


S 


H    r'r 


/7s 


Writing  for  String  Quartet 


247 


While  working  out  the  above  design  a  constant  endeavor 
should  be  made  to  treat  the  voices  in  imitative  counter- 
point. At  the  same  time  the  style  must  be  natural  and 
flowing.  Portions  or  modifications  of  either  one  of  the 
chief  motives  can  often  be  introduced  with  good  result. 
All  the  voices  need  not  be  kept  going  throughout.  Rests 
are  often  the  best  preparation  for  the  effective  entrance  of 
an  important  melodic  phrase. 

§179.  Two  short  basses  are  now  given,  to  which  three 
upper  voices  are  to  be  written  in  free,  rhythmically  varied 
counterpoint.  Work  of  this  kind  affords  practice  of  the 
highest  value.  The  composer  Rossini,  as  is  well  known, 
taught  himself  harmony  by  an  analogous  method.  He  was 
accustomed  to  copy  the  cello  (bass)  part  of  a  Haydn  quar- 
tet, and  then,  after  racking  his  ingenuity  to  conjecture 
what  interesting  upper  voices  might  be  implied  by  the 
bass,  to  compare  carefully  his  own  version  with  the 
original.  In  truth,  there  could  hardly  be  a  better  method 
of  gaining  facility  of  expression. 

Quoted  from  PROUT 


Quoted  from  PROUT 
ifa 


CHAPTER    XIII 
Supplementary  Exercises  in  Various  Styles 

§  1 80.  We  now  give  a  last  set  of  supplementary  exercist 
to  be  treated  either  for  voices  or  for  strings,  in  which  the 
style  should  be  as  free  as  possible;  that  is,  the  student 
should  endeavor  to  introduce  into  the  harmonization  all  the 
devices  of  imitation,  varied  rhythm,  syncopation,  etc.,  by 
which  part-writing  is  made  more  organic  and  more  full 
of  interest.  Especial  care  should  be  paid  to  the  exercises 
in  which  the  melody  is  in  the  alto  or  the  tenor  voice. 
Whether  written  for  voices  or  strings,  the  arrangement  of 
clefs  for  a  string  quartet  had  better  be  preserved,  as  the 
musician  can  hardly  have  too  much  practice  in  this  form 
of  open  score. 

"!_.     Andante  con  moto 


§181.  In  this  simple  diatonic  melody  an  elaborate  rhyth- 
mical scheme  would  be  out  of  place.  An  even,  flowing 
motion,  however,  should  be  sustained,  especially  at  the  end 
of  the  phrases.  A  short  melodic  phrase  repeated  in  the 
different  voices  will  help  to  give  unity  to  the  treatment. 
The  melody  might  be  commenced  as  follows: 


etc*. 


Supplementary  Exercises 


249 


Observe  that,  although  the  harmonic  scheme  is  very  simple 
and  natural,  by  crossing  the  inner  voices  at  (a)  an  inter- 
esting downward  phrase  is  secured  for  the  alto,  while  the 
short  motive  with  which  the  bass  begins  is  imitated  in 
several  of  the  other  voices. 

Same  melody  in  the  alto: 


$=&=$= 

9 
jP    ^ 

im  —  t—  o  — 

o            " 

1           1 

(- 

^ 

-H  — 

o 

• 

etc. 

Hi 

n 

/  »    g 



1 

• 

'•° 

3. 


Same  melody  in  the  tenor : 


ZiES 


I 


t*  "i/ 


K'TP'g  » 


e/c. 


This  melody,  with  its  numerous  thirds,  is  not  practica- 
ble in  the  bass.  The  following  melody,  however,  is  capa- 
ble of  satisfactory  treatment  in  each  voice : 


250 


Tonal  Counterpoint 

etc.  with  a  different  harmonic  scheme 


At  (a)  observe  that  the  parallel  fifths  between  the  soprano 
and  tenor  are  not  of  harmonic  import  as  the  g#  in  the 
soprano  is  a  passing  note. 


5. 


Same  melody  in  the  alto: 


fr/t/Crrr 


^ 


t 


^f«"  MI  rmrprr 


Same  melody  in  the  tenor : 


^ 


efc. 


d     •'a* 


ttc. 


Supplementary  Exercises 
Same  melody  in  the  bass : 


251 


The  following  melody  may  likewise  be  treated  effectively 
in  each  voice: 


8. 


^ 


p 


s 


^ 


^p 


nrr'^j? 


This  same  melody  in  the  alto  is  entirely  worked  out  to 
serve  as  a  model  for  subsequent  treatment  in  the  tenor. 


^=^ 


^^ 


It 


252 


Tonal  Counterpoint 
>*^ 


m 


^m 


m 


Same  melody  in  the  tenor: 


Supplementary  Exercises 
Same  melody  in  the  bass: 


253 


^ 


m 


Let  the  student  ask  himself  what  is  the  justification  for 
the  parallel  fifths  at  (a). 

Moderate     12. 


"B/  lay 


§  182.  This  is  a  melody  rather  modal  than  strictly  towa/  in 
character,  especially  in  the  cadence  implied  at  the  end  of 
the  second  phrase  at  (a).  It  should  be  treated  in  the  strict 
style;  that  is,  the  harmonic  basis  should  consist  largely  of 
the  fundamental  triads,  varied  by  suspensions,  accented 
passing  notes,  etc.  Nothing  as  yet  has  been  said  about  the 
ecclesiastical  or  old  modes,  and  in  such  a  brief  treatise  we 
can  hardly  touch  upon  so  exhaustive  a  subject.  The  well- 
informed  student,  however,  should  know  something  of 
them,  especially  of  the  ^olian,  the  Dorian  and  Phrygian 
modes,  for  traces  of  these  are  often  found  in  modern  music. 
The  ^Eolian  mode  is  practically  our  minor  scale  without 
the  raised  leading  tone  for;  example, 


§183.   The  Dorian  mode  is  the  scale  on  the  white  keys  of 
a  pianoforte,  starting  on  d;  that  is, 


f 


254 


Tonal  Counterpoint 


although  little  by  little,  as  the  need  for  a  leading  tone  was 
felt  —  to  gain  a  major  triad  on  the  dominant  —  the  c  was 
sharpened.*  The  characteristics  of  this  mode  as  commonly 
used  are  the  minor  third  and  the  major  sixth.  The  well- 
known  choral,  "Jesu,  meine  Freude,"  is  a  fine  example  of 
a  melody  in  the  Dorian  mode.f 


The  Phrygian  mode  is  the  following: 


§184.  The  student  should  compare  it  carefully  with  the 
Dorian.  In  this  mode  we  find  both  the  third  and  the  sixth 
minor,  but  the  really  characteristic  note  which  distinguishes 
it  from  all  the  other  modes,  and  which  produces  such  a 
striking  effect  when  introduced  into  modern  music,  is  the 
minor  second.  This  note  in  connection  with  the  whole  tone 
below  the  tonic,  for  example, 

1 


gives  such  a  modal  effect  when  used  in  a  cadence  that  com- 
binations of  chords  like  the  following  are  always  spoken  of 
as  Phrygian  cadences: 


PH 

4-, 

| 

&l  — 

1)  —  1 

t 

^=, 

J 

,(j»o 

r    r 
JJ, 

'r 
j 

TS 
^R= 

t 

\   , 

J 

-e- 

Observe  that  the   last  chord  by   chromatic   alteration  is 
made  major.     This  was  always  the  case  except  in  the  most 

*  Consult  the  article  "Musica  Ficta,"  in  Grove's  Dictionary,  Vol.  II. 
t  See,  also,  Bach's  great  organ  fugue  in  the  Dorian  mode. 


Supplementary  Exercises 


255 


ancient  plain  song  usage.  For  an  example  of  a  melody 
in  the  Phrygian  mode,  seethe  choral,  "O  Haupt  voll  Blut 
und  Wunden." 


-yf—&  — 

— 

i  j  j 

i  — 

§**  i 

= 

i  «*  j  . 

* 

^=* 

3 

For  a  most  impressive  use  of  this  mode  in  modern  music, 
see  the  slow  movement  of  Brahms'  Fourth  Symphony, 
which  begins  with  this  phrase  intoned  by  the  horns  and 
wood-wind : 

,4  ndante  moderate 


The  contrast  effected  by  the  introduction  of  our  modern 
E  major  scale  at  the  fourth  measure  is  truly  sublime.  To 
return  to  our  melody  in  G  minor  the  student  will  now 
understand  that  the  end  of  the  second  phrase  should 
be  harmonized  with  a  Phrygian  cadence,  for  the  notes 


correspond  exactly  with 


inn 


25$ 


Tonal  Counterpoint 


The  first  two  phrases  are  worked  out  as  a  model  for  sub- 
sequent treatment.  In  the  last  part  of  the  melody  imita- 
tive phrases  can  be  used  with  good  effect. 


fel 


*     * 


e/c, 


p 


* 


Observe  the  effective  use  made  of  syncopation  at  (a),  (6) 
and  (c).  This  device  often  serves  to  keep  up  the  rhythm. 
At  (d)  the  plain  Phrygian  cadence  is  varied  by  an  accented 
passing  note  and  an  auxiliary  note  in  the  alto  and  tenor. 
The  same  melody  is  now  treated  in  the  alto  with  the  sys- 
tematic introduction  of  a  secondary  motive,  which  is  imi- 
tated in  the  several  voices : 

etc. 


¥ 


^ 


•ffft? 


m 


The  same  melody  in  the  tenor : 
14. 


I 


^ 


m 


i? 


rtr. 


Supplementary  Exercises 


257 


Observe  and  account  for  the  parallel  fifths  at  (a)  between 
soprano  and  tenor.  This  melody,  when  in  the  bass,  may 
be  treated  effectively  with  imitative  counterpoint. 

15. 


The  last  phrase  should  be  altered  as  follows,  in  order  to 
secure  a  proper  foundation  for  a  satisfactory  cadence. 


§  185.  The  student  who  has  worked  faithfully  at  the  vari- 
ous modes  of  contrapuntal  treatment  set  forth  in  this  book 
is  now  ready  to  take  up  the  more  complicated  forms  of  poly- 
phonic music :  canon,  fugue,  and  free  thematic  music,  —  such 
as  the  development  portion  of  a  sonata  form.  Those  who 
have  developed  a  strong  desire  to  write  some  original  music 
of  their  own  should  study  the  sonata  form,  and  also  the 
shorter  forms  of  instrumental  music,  —  the  prelude,  noc- 
turne, etude,  rondo,  the  various  dance  forms,  the  scherzo, 
etc.  The  work  for  a  progressive  musician  will  henceforth 
be  of  two  kinds:  First,  he  must  faithfully  cultivate  readi- 
ness of  imagination  and  facility  of  expression  by  constant 
attempts  at  original  composition;  and  second,  he  must 
stimulate  his  fancy  and  improve  his  style  by  the  study  and 
analysis  of  the  great  works  of  musical  literature,  both 
ancient  and  modern.  His  early  attempts  at  composition 
may  be  rather  eclectic  and  sound  like  the  music  of  the  com- 
posers he  has  studied.  This,  however,  in  itself,  is  not  a  bad 
sign.  Beethoven's  first  compositions  were  largely  in  the  style 
of  Haydn  and  Mozart.  Wagner  at  first  modeled  his  style 
on  Von  Weber.  A  few  particularly  good  compositions  are 
hereby  recommended  for  study  with  reference  to  wealth 
of  harmony  as  well  as  contrapuntal  style:  The  finale  of 


Tonal  Counterpoint 

Beethoven's  Third  Symphony,  the  first  and  last  move- 
ments of  Mozart's  G-Minor  Symphony,  the  first  movements 
of  Schumann's  Symphonies  in  C  major  and  in  D  minor, 
the  first  movement  of  Brahms'  Symphony  in  C  minor, 
and  Wagner's  Overtures  to  the  "  Meistersinger "  and  to 
"Parsifal." 

§186.  This  small  book  makes  no  pretense  to  be  an  ex- 
haustive treatise,  or  to  dictate  to  the  student  the  only  way  in 
which  he  may  become  an  original  composer  or  a  well- 
informed  musician.  Musical  art  is  continually  progressing; 
new  harmonies  are  being  discovered  and  accepted,  new  forms 
of  construction  are  being  developed  and  found  to  be  satis- 
factory. In  art  as  in  morals,  "He  must  ever  up  and 
onward  who  would  be  abreast  of  Truth."  The  young  musi- 
cian is  advised  not  to  worry  too  much  at  first  whether  his 
work  is  beautiful  or  not;  tnat  is  often  a  very  difficult  ques- 
tion to  settle,  and  is  often  decided  only  by  succeeding  gen- 
erations. But  whatever  he  does  must  be  sincere,  it  must 
come  from  his  heart,  and  the  workmanship  must  be  as  per- 
fect as  intelligent  and  steady  work  can  possibly  make  it. 
Genius  has  been  defined  as  "  an  infinite  capacity  for  taking 
pains."  The  composer,  no  matter  how  slight  the  effort, 
must  have  something  to  say,  and  he  must  know  how  to  say 
it  in  such  a  way  that  an  intelligent  and  receptive  hearer 
can  derive  pleasure  and  edification  therefrom.  Let  the 
student's  motto  be,  "  Test  all  things;  hold  fast  that 
which  is  good." 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 
This  book  is  DUE  on  the  last  date  stamped  below 


NUV  *  0  i* /I 


FEB  2  7  1975 


MAR  1 3  1975 

REC'O 


APR  5" 


MAR  3  1 
HAR311971 


R  1  JL  1974 
MAR  111974 


MAY  2 

••• 


NOV     61974 
NOV  -  8  1974 


FEB  1  3  1975 


MAR  2  8  1975 

APR -3  1975 

JAN  2 1 1976 


MUS-l* 

'AY  131976 
o  1976 


Form  L9-39, 050-8, '65 (P6234s8) 4939 


A     000146071     6 


MU51 

LIBHA 


